While the Federal Communication Commission limits how much radiofrequency radiation can come out of your cellphone, the Food and Drug Administration can have a say about whether those limits are safe. So the FDA asked the National Toxicology Program (NTP), a division within the National Institutes of Health, to investigate. Based on the NTP’s results, as well as hundreds of other studies, the FDA is still confident that the current limits on cellphone radiation are safe, according to a statement from Jeffrey Shuren, the director of the FDA’s Center for Devices and Radiological Health.
Then there is non-ionizing radiation, which encompasses the vast majority of light we are exposed to: visible light from lightbulbs, infrared light from an oven and from people, gigahertz light from our wifi, megahertz light to/from our cell phones, and radio waves hitting our car radio. They are not harmful in small doses because one photon does not have enough energy to ionize atoms and/or break apart molecules. In very large doses, non-ionizing radiation can be harmful. For example, a visible light laser with sufficient power (at least several hundred times more than a legal laser pointer) which is concentrated in a small enough spot will burn your skin and do worse things to your eye if it gets in there. And those of us who are old enough, remember the gerbil-in-a-microwave flash animations which went viral 17 years ago [1] as a humorous (but not exactly factual) representation of what would happen if you microwaved a live rodent.
The papers found that, in male rats, there was “clear evidence” that exposure to cell phone radiation increased risk for a rare type of malignant tumor called schwannoma in the connective tissues that surround nerves in the heart (they found “equivocal” evidence for the same thing in female rats). They also found “some evidence” that the radiation caused malignant glioma—a type of brain cancer affecting glial cells—in the male rats.

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.
“We see either no change or very small increases in incidence in some tumor types,” Quinn Ostrom, the Baylor College of Medicine researcher who has been analyzing these cancer trends, explained. “I would be inclined to say this isn’t as much of an increase as you might expect if cellphones were causative [of brain tumors] due to the very sharp way use of these devices has gone up over the last 20 years.”

But scientists disagree on how real—or how serious—these risks really are, and studies have not established any definitive links between health problems and radiofrequency (RF) energy, the type of radiation emitted by cell phones. “This document is intended to provide guidance for people who want to reduce their own and their families’ exposure to RF energy from cell phones,” the guidelines state, “despite this uncertainty.”
The European Union is currently running the Mobi-Kids, a case-control study in 14 countries, to better understand the effects of electromagnetic fields radiation on children and adolescents. One of the early publications from the project, looking at data on the use of wireless devices among 10- to 25-year-olds in France, found that kids are started to rely on these devices earlier and earlier in life. But the researchers are still analyzing the main results on any health impacts, and haven’t yet published their findings.

It’s true that cellphones do emit radiation. And radiation is a scary word for a lot of people, thanks in part to the horrific aftermath of nuclear accidents and photographs of victims of the nuclear bombs the US dropped on Japan in World War II. People hear radiation and they associate it with nuclear radiation and the bomb, says Geoffrey Kabat, a cancer epidemiologist at the Albert Einstein College of Medicine and author of the book Getting Risk Right. “There are all these associations and those are deeply ingrained in people. But it doesn’t apply here.”
Scientists have reported adverse health effects of using mobile phones including changes in brain activity, reaction times, and sleep patterns. More studies are underway to try to confirm these findings. When mobile phones are used very close to some medical devices (including pacemakers, implantable defibrillators, and certain hearing aids) there is the possibility of causing interference with their operation. There is also the potential of interference between mobile phones signals and aircraft electronics. Some countries have licensed mobile phone use on aircraft during flight using systems that control the phone output power.
According to Dr. Devra Davis, who wrote Disconnect: The Truth About Cell Phone Radiation, cell phones are dangerous because they emit erratic signals capable of disrupting resonance and DNA repair. As long as your cellular phone is on, it sends out radiation intermittently. Even if you don’t take your phone out of your pocket all day, it continues to expose you to radiation. Dr. Joseph Mercola, founder of Mercola.com recently wrote an excellent article on the dangers of cell phones and provided common sense ways we can protect ourselves and our family from the electromagnetic radiation it emits.
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]
Bonus application! In addition to shielding magnetic fields, PaperSHIELD is also quite good at shielding radiowaves (cellphone, wifi, etc). And because of the adhesive backing, it can be adhered to almost any surface you need such as the inside or back of your cellphone case. (Use a near field meter to test RF shielding performance.) Note that it is not transparent, so it can't be used on the touch screen side. Cover the cut edges with sturdy tape as they can be sharp. 36 inches wide. Made in USA.
Educate yourself about the RF sources in your home, and replace the devices that you can with non-wireless alternatives, and replace the wireless connections that you can with wired ethernet or other cord/cable connections. Note: most wireless devices can connect non-wirelessly, sometimes an easy-to-find adaptor accessory is required to use cords/cables.
The frequency of radiofrequency electromagnetic radiation ranges from 30 kilohertz (30 kHz, or 30,000 Hz) to 300 gigahertz (300 GHz, or 300 billion Hz). Electromagnetic fields in the radiofrequency range are used for telecommunications applications, including cell phones, televisions, and radio transmissions. The human body absorbs energy from devices that emit radiofrequency electromagnetic radiation. The dose of the absorbed energy is estimated using a measure called the specific absorption rate (SAR), which is expressed in watts per kilogram of body weight.