Among the hundreds of smartphone cases available for iPhone and a bevy of popular Android phones, there are some that claim to reduce the amount of radiation your body absorbs when you have the handset close to your body. Pong Research is a US brand that offers a range of products fitting this description, as is Cellsafe, a company based in Victoria, Australia.
If you paid an electrical engineer to shield something for you, depending on the application, they would either use MuMetal or this type of mesh shielding. It’s not some new technology, so there’s no question of whether it works, because it does. Regardless, it would still be nice for them to publish third-party independent testing to reassure people of this.

The most common effect is heat generation (though non-thermal biological harm has also been demonstrated), which can alter the characteristics of various bodily tissues depending on the amount of radiation present and its ability to penetrate the body. Tissue damage can promote the cellular mutations and increase your long-term risk of developing cancer.
Using a speaker/personal speakerphone or earplug (not wireless) during conversation - distancing the mobile phone from the user’s body reduces his exposure to the radiowave radiation. Therefore, keep the mobile phone at a distance from the body (do not carry it on the body, such as in the belt, pocket or on a neck strap). Obviously, reducing the amount and duration of calls on the mobile phone is another simple measure to reduce exposure.
There are ongoing worries about whether cellphones can give you cancer — especially brain cancer, since our phones spend so much time near our faces. It’s true that cell phones do emit radiation. But it’s radiofrequency radiation, which is much lower energy than the ionizing radiation you’d get from an X-ray, or, say, nuclear fallout. Ionizing radiation can cause DNA damage that can eventually lead to cancer. But the radiofrequency radiation from a cellphone doesn’t work that way — and today’s results support that.

“The exposures used in the studies cannot be compared directly to the exposure that humans experience when using a cell phone,” John Bucher, a senior scientist at the NTP, a government program within the department of Health and Human Services, says in a press release. “In our studies, rats and mice received radio frequency radiation across their whole bodies. By contrast, people are mostly exposed in specific local tissues close to where they hold the phone. In addition, the exposure levels and durations in our studies were greater than what people experience.”
To check for radiowave emissions, use an RF meter with Near Field antenna. Again, position the antenna loop on the phone (because the entire antenna stem has some sensitivity, it is best to position the entire antenna over the area that will be shielded). Note carefully where the loop is positioned. Make a call and watch the readings. Notice the highest and lowest readings, and make a mental note of the "average" reading. Now, insert the shield, and repeat.
To be fair I haven’t tried every single one on the list, but that just be careful in investing your sense of security, let alone good health, in a misplaced sense of something working just because someone says it does and they have “studies” to prove it. Every single company now claims “independently scientific studies” where as this is just usually falsified information and a marketing tactic.

The study specifically used 2G and 3G frequencies — not the frequencies used on more advanced 4G or 5G networks. Researchers exposed the rodents’ entire bodies to the radiowaves for more than nine hours per day, for up to two years. (“A rat that is 2 years old is roughly equivalent to a 70-year-old person,” STAT News reports.) These exposure levels were much higher than what people would experience, John Bucher, senior scientist with the NTP, says in a statement. “So, these findings should not be directly extrapolated to human cell phone usage,” he says.
An analysis of data from NCI's Surveillance, Epidemiology, and End Results (SEER) Program evaluated trends in cancer incidence in the United States. This analysis found no increase in the incidence of brain or other central nervous system cancers between 1992 and 2006, despite the dramatic increase in cell phone use in this country during that time (22).
The World Health Organisation (WHO) released a fact sheet about these issues, shortly after the IARC re-classification, entitled "Electromagnetic fields and public health: mobile phones". The fact sheet points to the findings of the IARC and describes some of the known short-term and long-term effects of phone use, but ultimately, it lands on the side of where the most conclusive evidence exists:
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Considering the current standards in the State of Israel and due to the distance from the base stations, the radiation that reaches people from this source is extremely low. Although direct studies that will test the effects of antennas on human health are not feasible, considering the aforesaid, this probably does not pose a significant health risk.
The authors of these studies noted that the results were preliminary and that possible health outcomes from changes in glucose metabolism in humans were unknown. Such inconsistent findings are not uncommon in experimental studies of the biological effects of radiofrequency electromagnetic radiation in people (4). Some factors that can contribute to inconsistencies across such studies include assumptions used to estimate doses, failure to consider temperature effects, and lack of blinding of investigators to exposure status.

SafeSleeve Anti Radiation Case: Safe Sleeve website says they integrate FCC accredited independent lab tested "shielding technology" in their products. There are many links to "SafeSleeve, Is it a Scam?" and "Does SafeSleeve work?" online, but if you follow those links you'll find they go to the actual SafeSleeve site where the question of SafeSleeve protection is addressed.  You'll see in this demonstration that the radiation level was higher with the SafeSleeve Case on.
The guidelines recommend keeping phones away from the body when they’re not in use—in a backpack, for example, rather than a pocket—and sleeping with phones away from the bed. People may also choose to use speakerphone or a headset to make calls, rather than holding the phone to their heads. (They should remove their headsets when they’re not in use, though, as these devices also emit small amounts of RF frequency.)

If you want to measure the EMF radiation from your own phone, and know if EMF protection products are working, you should get a quality EMF meter. I highly recommend the new TriField TF2 (read my review) as it’s simple to use, lasts forever, is extremely accurate, and measures all three types of EMF radiation. If you’re looking for a low-cost EMF meter I really like the Meterk (read my review).

The electromagnetic spectrum is broken up into two parts based on whether small doses of that radiation can cause harm: ionizing radiation and non-ionizing radiation. Ionizing radiation—UV, x-rays, and gamma rays—has enough energy in one photon (quantized minimum packet of light) to remove electrons from atoms or break apart chemical bonds. It is because of this potential for cancer-causing DNA damage that you wear a lead vest when you get x-rays at the dentist and you are advised to wear sunblock when you go out in the sun. One can’t avoid natural (radon, cosmic rays when you are up in an airplane) and man made (diagnostic x-rays) sources of ionizing radiation completely, but it is reasonable advice to minimize exposure when possible.
The reason we’re talking about cellphones and cancer — why there’s a concern here — is because they emit radiation, the invisible waves of electric and magnetic energy, of varying power, organized on the electromagnetic spectrum. You can see in the graphic below that less powerful (or lower-frequency) types of radiation are on the left, moving to the more powerful (or higher-frequency) types of radiation on the right.
What the study showed: Self-reported cell phone use was not associated with an increased risk of glioma, meningioma, or non-central nervous system tumors. Although the original published findings reported an association with an increased risk of acoustic neuroma (14), this association disappeared after additional years of follow-up of the cohort (15).