Stick on anti-radiation protection shields etc are often made of metal which may block signal and prevent reliable mobile phone communications with signal towers. Mobile phones recognise the potential for a dropped signal and actually increase power to compensate. The result is a fast draining battery and an even higher radiation output as a result of using the product (an exception to this are shields that are placed in between the phone and the user as these do not impede signal to cell towers to any significant degree)
I really want to caution you to be careful of any "expert" or EMF blogger recommending anti-radiation filtering cases, stickers that attach to the phone or necklaces to "ward off" EMF.  I get it, when I first realized 25 years ago that I was sensitive to electromagnetic energy and then later, when I understood that without a doubt, man made electromagnetic radiation has a biological effect on my body, I wanted an easy fix.  I tried the shielding materials and cases and I just did not feel any better.  Then I bought meters to see if the energy changed and I actually noticed what the California Department of Health now says and it's what the FTC and FCC post warnings about:  "Some shielding materials can make exposures worse". So please, be careful and read on for what you can do to avoid electromagnetic radiation exposure.

When it comes to ionizing radiation — which we’re exposed to in X-rays, in CT scans, and during air travel — we know it’s powerful enough to damage the DNA, and that repeated DNA damage over time can cause cancer. That’s why, for example, you’re not supposed to get too many X-rays in your lifetime. (In case you were wondering, there’s no precise number on how many X-rays are too many — but the Food and Drug Administration suggests keeping track and avoiding any that seem unnecessary.)

Of course, scientific seesawing like that doesn’t provide a lot of clarity or confidence for the 90 percent of American adults and roughly 80 percent of teens who report having a cell phone. So how concerned should you be about cell-phone radiation? Consumer Reports’ health and safety experts conducted a thorough review of the research and offer some guidance.

Dr. Carlo, however, refused to be an easy target. He quickly recruited a group of prominent scientists to work with him, bulletproof experts owning long lists of credentials and reputations that would negate any perception that the research was predestined to be a sham. He also created a Peer Review Board chaired by Harvard University School of Public Health’s Dr. John Graham, something that made FDA officials more comfortable since, at the time, the agency was making negative headlines due to the breast implant controversy. In total, more than 200 doctors and scientists were involved in the project.

We did not simply measure energy coming from the front of the case which is the area of the case where the phone would be "shielded" from radiation. If we had taken readings with a directional meter, specifically measuring energy coming from only the front or flap cover where the shielding material is, we assume as the manufacturers claim, that we would have seen a drop in the radiation readings.
Leibovich was very careful to point out in our interview that Cellsafe is not claiming that the radiation absorbed by the body during phone use leads to health issues like brain tumours, male infertility or damage to unborn babies. But the Cellsafe website strongly suggests these links. Its homepage (image below) leads with the phrase "You should be concerned!" in an eye-catching red, and there is as much screen real estate on the site dedicated to information about the dangers of radiation, as there is for descriptions of the Cellsafe products. This information refers to "high levels of RF radiation" in several places, but it doesn't say whether this describes radiation from phone use.
Could you please provide me with evidence that non-ionizing radiation is damaging to humans? In another post illustrating the threats of non-ionizing radiation you have said that this radiation is damaging to children, and link an article by the American Academy of Sleep Medicine. However, this linked page contains no mention of non-ionizing radiation, and instead suggests that children are simply addicted to use of mobile phones, thus using them instead of sleeping. You also provided a link to a PubChem page on the negative effects of this radiation, but this page appears to no longer exist.
The cell phone industry constantly guards its financial interests, but unfortunately, an unwitting public can be harmed in the process, says Dr. Carlo. “Industry-funded studies in many cases now produce industry-desired outcomes. By tampering with the integrity of scientists, scientific systems and public information steps over the lines of propriety that are appropriate for protecting business interests—especially when the casualty of the interference is public health and safety.”

Pong’s research indicates that badly designed cell phone cases can partially block a phone’s antenna, making the device work harder to transmit signals. Due to gaps in the FCC’s cell phone regulations, a phone worn right next to the body and enclosed by a case that obstructs the antenna could expose the user to more radiation than the FCC’s legal limit.
The International Agency for Research on Cancer (IARC) is part of the World Health Organization (WHO). Its major goal is to identify causes of cancer. The IARC has classified RF fields as “possibly carcinogenic to humans,” based on limited evidence of a possible increase in risk for brain tumors among cell phone users, and inadequate evidence for other types of cancer. (For more information on the IARC classification system, see Known and Probable Human Carcinogens.)
RadiArmor’s anti-radiation material blocks over 99% of EMF radiation. However, since covering your entire phone with this material would result in no reception, only the front cover is lined with this material. This still provides an effective EMF reduction of 91% with no loss in reception. The front cover has a hole for sound to pass through so that you can close the case and talk at the same time.
Today there are more than two billion cell phone users being exposed every day to the dangers of electromagnetic radiation (EMR)—dangers government regulators and the cell phone industry refuse to admit exist. Included are: genetic damage, brain dysfunction, brain tumors, and other conditions such as sleep disorders and headaches.1-9 The amount of time spent on the phone is irrelevant, according to Dr. Carlo, as the danger mechanism is triggered within seconds. Researchers say if there is a safe level of exposure to EMR, it’s so low that we can’t detect it.
Moving the meter around the case, we detect readings on the side, back and front of the case. We use the multi-directional TES 593 meter which measures 10 MHz to 8GHz. We use the unit of micro-watts per square centimeter, which looks like this little symbol: μW/cm² and we use it on the max setting which shows the maximum measured value. In non-science speak: the highest level of RF we see, which could be from the back the side or the front. 
Toward the end of 1998, Dr. Carlo’s house mysteriously burned down. Public records show that authorities determined the cause of the blaze was arson, but the case was never solved. Dr. Carlo refuses to discuss the incident and will only confirm that it happened. By this time, enough was enough. Dr. Carlo soon went “underground,” shunning the public eye and purposely making himself difficult to find.
Anyway, several phone models that my wife and I considered buying emitted radiation levels simply too high for my comfort level. They’re measured in SAR -- “specific absorption rate” -- which is essentially the amount of radiation a human body will absorb from using or being near a cell phone. The lower the rate, the less radiation will be absorbed.
A large, long-term study has been comparing all of the people in Denmark who had a cell phone subscription between 1982 and 1995 (about 400,000 people) to those without a subscription to look for a possible increase in brain tumors. The most recent update of the study followed people through 2007. Cell phone use, even for more than 13 years, was not linked with an increased risk of brain tumors, salivary gland tumors, or cancer overall, nor was there a link with any brain tumor subtypes or with tumors in any location within the brain.
In March, however, a peer-review panel of 11 experts from industry and academia voted to advise the agency that it should raise the confidence level from “equivocal evidence” to “some evidence” of a link between cellphone radiation and brain tumors in male rats. (The female rats did not show evidence of a link between the radiation and such tumors.) Two panel members, Lydia Andrews-Jones of Allergan and Susan Felter of Procter & Gamble, proposed the risk upgrade.
We are often asked why we don't carry the chips, neutralizers, cutesy bugs, and some other cellphone radiation products that are so heavily marketed on the internet. Our answer is simple and honest: our criteria for including a product in our catalog is that it does what we say it does, and its effectiveness can be demonstrated with an appropriate meter.
The base station is equipped with antennas for reception and transmission. In order to communicate, the mobile phones and the antennas at the base station emit radiowave radiation (see below). The mobile phone instrument transmits a lower amount of radiation than the one transmitted by the transmission center (cell site), but because the instrument is near the body, the body directly absorbs the energy from the instrument’s antenna.

As a rule, modern medical equipment is well protected against exposure to radiowave radiation. Therefore, there is generally no need for concern regarding the effects of mobile phones on the normal function of the equipment. Nevertheless, the Ministry of Health recommends not to have a mobile phone in the immediate proximity (a distance of 30-50 cm from the portable medical equipment or from medical equipment implanted in the patient's body).
So what do you do when you need a wireless radiation emitting device but you want to limit the exposure to the people? Perhaps you use a wireless baby monitor, have a cordless phone base station, or you sleep with your cell phone on your nightstand. Maybe there is a wifi router right next to you at work or school. RadiaFence is the answer. It’s a free-standing, semi-transparent microwave barrier that you can put almost anywhere you need. It blocks most of the radiation emitted in one direction by “casting a shadow” (typically 70-90% reduction), while still allowing the wireless device to work. Like sitting in the shade on a sunny day. Portable, inexpensive, attractive. And it couldn’t be easier to use. If you like, you can add a decorative photo or warning sign to change the appearance. Available in 5 styles. Pick the sizes which meet your needs. Style may differ from images.
The government, however, does not require phone manufacturers to consider the effect of cases when they conduct compliance tests to meet the FCC’s allowable radiation exposure limits. The significance of this omission was underscored by tests commissioned by case-maker Pong Research and submitted to the FCC in May 2012. Those tests showed that three models of cases made by competing companies and used with an iPhone4 increased the phones’ Specific Absorption Rate, or SAR – the amount of radiation absorbed by the user’s body – by 20-to-70 percent (Table 1).
An analysis of data from all 13 countries participating in the Interphone study reported a statistically significant association between intracranial distribution of tumors within the brain and self-reported location of the phone (7). However, the authors of this study noted that it is not possible to draw firm conclusions about cause and effect based on their findings.