At high power levels, RF waves can heat up water molecules (which is how microwave ovens work). Scientists used to focus their concerns on the possibility that such heating of human tissue, which is mostly water, might damage cells. In fact, the FCC’s test of cell-phone emissions—which was set in 1996 and which all phones must pass before being allowed on the market—is based on that effect.

We tested the garments in a similar setup with the fabric between the phone and the meters. We also tested the garments while sitting on a couch, holding the Gigahertz Solutions monitor against my pregnant belly under the product (blanket/nursing cover) and measuring the reduction of the RF from my cellphone in my hand at normal texting/web-surfing distance.

Introducing, SafeSleeve for Cell Phone. A patent pending, elegant, and stylish solution that seamlessly combines Anti-Radiation and Anti-RFID technology with an impact and scratch resistant case. We've also added an RFID blocking wallet and a built-in stand for peace of mind and convenience. It’s basically the Swiss Army knife of cell phone cases, but with Anti-Radiation Technology instead of that plastic toothpick. 
Just take a moment and think about how much you’re using your phone every single day. Answering calls, discussing plans, talking about your day with friends, playing games, watching videos and using apps, only scratch the surface of how much you’re actually using your phone. You might even have it by your bedside or on your nightstand when you go to bed at night. It’s time you stopped exposing yourself to dangerous EMF radiation and protected yourself from the dire consequences of using an unshielded smartphone or tablet.
Your phone sends radiofrequency, or RF, waves from its antenna to nearby cell towers, and receives RF waves to its antenna from cell towers when you make a call or text or use data. The frequency of a cell phone’s RF waves falls between those emitted by FM radios and those from microwave ovens, all of which are considered “non-ionizing” forms of radiation. That means that—unlike radiation from a nuclear explosion, a CT scan, or a standard X-ray—the radiation from your phone does not carry enough energy to directly break or alter your DNA, which is one way that cancer can occur. (FM radios and microwaves don’t raise alarms, in part because they aren’t held close to your head when in use and because microwave ovens have shielding that offers protection.)
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.
In order to protect the population living around base stations and users of mobile handsets, governments and regulatory bodies adopt safety standards, which translate to limits on exposure levels below a certain value. There are many proposed national and international standards, but that of the International Commission on Non-Ionizing Radiation Protection (ICNIRP) is the most respected one, and has been adopted so far by more than 80 countries. For radio stations, ICNIRP proposes two safety levels: one for occupational exposure, another one for the general population. Currently there are efforts underway to harmonise the different standards in existence.[26]

Consumers should utilize an air tube headset as a safer alternative to wired headsets or in-ear Bluetooth headsets, use the speaker feature and keep phones away from your body unless there is RF radiation shielding between the wireless device and cell phone users body.  When carrying a phone on your body it’s highly recommended to use either an RF Safe flip cover radiation shielded phone case or pocket shield to deflect excessive radiation away.
The bulk of scientific evidence says that cellphone radiation doesn’t harm humans, according to the Food and Drug Administration: our cellphones are much more likely to kill us when we glance down at them while driving. But people are bad at judging risk. And the word “radiation” combined with the fact that we can’t see or control the invisible forces emanating from our cellphones becomes a perfect recipe for fear.
So you decided you are going to use your cell phone in your car, despite all the warnings. But you have the good sense to keep it away from your head and body! This handy mount can securely hold your phone, iPod, MP3 player or GPS unit with confidence as your drive. Allows easy access and a clear view. Can be used by anyone in the car: driver, passenger, or even in the back seat. Plugs securely into a cup holder and is fully adjustable to any position. Cradle adjusts and can securely accommodate devices up 3.5 inches wide. Completely hands free. Can also be used on boats, recliners or anywhere a cup holder is waiting. You can even do his’n’hers!
Cell phones emit low levels of radio frequency energy (i.e., radio frequency radiation) in the microwave range while being used. It is well known that high levels of RF can produce biological damage through heating effects (this is how your microwave oven is able to cook food). However, it is not known to what extent or through what mechanism, lower levels of RF might cause adverse health effects as well. Several research studies have shown that the radio frequency radiation from wireless phone antennae “appears to cause genetic damage in human blood,” while another case study uncovered a “statistically significant increase” in neuro-epithelial brain tumors among cell phone users. Other research has shown little or no adverse effects. ABC’s 20/20 News (May 26, 2000) took the five most popular phones sold in the US and tested them at a highly respected German laboratory. Four out of the five phones tested were above the SAR limit. One thing is for certain, similar to the case of cigarette smoking, it will take several tests and many years before the effects of radio frequency radiation on the human body are known.

“The near field plume is the one we’re most concerned with. This plume that’s generated within five or six inches of the center of a cell phone’s antenna is determined by the amount of power necessary to carry the signal to the base station,” he explains. “The more power there is, the farther the plume radiates the dangerous information-carrying radio waves.”
The study also found that about 5 to 7 percent of the male rats exposed to the highest level of radiation developed certain heart tumors, called malignant schwannomas, compared to none in the control group. Malignant schwannomas are similar to acoustic neuromas, benign tumors that can develop in people, in the nerve that connects the ear to the brain.
INTEGRITY: Many manufactures claim near 100% EMF protection, referring to the radiation blocking material, NOT the protection you receive on a call. If you covered your whole phone with EMF blocking material, then you'd have no signal. Our EMF blocking material is used on the front cover only, providing you real EMF protection with no sacrifice in reception.

The CERENAT study, another case–control study conducted in multiple areas in France from 2004 to 2006 using data collected in face-to-face interviews using standardized questionnaires (18). This study found no association for either gliomas or meningiomas when comparing regular cell phone users with non-users. However, the heaviest users had significantly increased risks of both gliomas and meningiomas.