The BlocSock is a small, 3”x5½”, lightweight case that's only designed for cell phones, not tablets or laptops. One side is a normal fabric to ensure reception. The other side has a rectangular, metallic mesh to shield RF radiation. It's recommended that you keep the side with the shielding material between the phone and your body. When making or receiving calls, keep the shielding between your head and the phone. It can also be moved into a smaller “kangaroo style” pouch during calls. It's effective, and tests show that it reduces RF exposure 96%. For more information, check out the SAR research test or watch this video.
There was also “equivocal” evidence that it raised the risk of heart conditions, and led to evidence of DNA damage. Baby rats born to mothers during the trial had lower birth weights. The scientists also found a statistically significant increase in lymphoma (cancer of the lymph nodes) among female mice and heightened rates of liver cancer in the male mice. All those findings were labeled “equivocal.”

DefenderShield Cellphone Radiation Case also claims independent testing and says in their website: That a "sophisticated layering of separate non-toxic, human safe materials processed for maximum radiation blocking efficiency. Each material has unique and targeted radiation-shielding characteristics designed to work in unison to eliminate all radiation emissions from 0 to 10 GHZ and Defender Shield technology refracts, conducts and finally absorbs all these potentially harmful emissions."  In this demonstration, the radiation level measured when DefendeShield case was on is still quite a bit above the level of exposure that I would recommend. I personally do not recommend-holding a phone with a shielding case to your head as the DefenderShield website shows a young woman doing as she demonstrates the product. 

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.
But, like the human studies, one can pick apart the NTP studies too. For one thing, the animals experienced cell phone radiation that was different from what humans live with. As Bucher said in a statement, “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.”
Pong’s claims for its case have stood up to the scrutiny of Wired magazine and the Better Business Bureau (Advertising Self-Regulation Council 2012; Ganapati 2009). In tests conducted by Cetecom, a cell phone radiation certification lab, and observed by a reporter from Wired magazine, an iPhone 3G tested without a case had a maximum SAR of 1.18 W/kg when held at the ear. The same phone tested with a Pong case had a maximum SAR of 0.42 W/kg (Ganapati 2009).  
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.
SafeSleeve's report is right up front about showing that they do not test or certify the Safe Sleeve case, rather they are simply testing the material they put into the case in a completely artificial environment, in a laboratory setting, using a signal generator and a power amplifier. Safe Sleeve includes photos showing how the measurements are taken. But that may not be how anyone will ever use their phone.
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.
As to increases in brain tumors tied to cell phone use, it’s too early to tell due to a lack of hard data, says Dr. Carlo. “We’re never going to see that in time to have it matter. Here in the US, we’re six years behind in getting the brain tumor database completed, and currently the best data are from 1999. By the time you see any data showing an increase, the ticking time bomb is set.”
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. 
According to the FTC, there is no scientific proof that so-called shields significantly reduce exposure from electromagnetic emissions. Products that block only the earpiece – or another small portion of the phone – are totally ineffective because the entire phone emits electromagnetic waves. Such shields "may interfere with the phone's signal, cause it to draw even more power to communicate with the base station, and possibly emit more radiation."[47] The FTC has enforced false advertising claims against companies that sell such products.[48]
The Ministry of Health Medical Administration circular (from 2002) addressed to hospital Directors, states that use of mobile phones and wireless handheld transceivers (walkie talkie) in the hospital, must on the one hand guarantee the patient’s wellbeing and safety, and on the other hand, allow the staff, the patients and their families to enjoy the service benefits. This circular outlines the areas where use of mobile phones is strictly forbidden and areas where use is permitted (while keeping an appropriate safety distance from areas where life-supporting equipment or systems are operated).
The World Health Organization states that "A large number of studies have been performed over the last two decades to assess whether mobile phones pose a potential health risk. To date, no adverse health effects have been established as being caused by mobile phone use."[2] In a 2018 statement, the FDA said that "the current safety limits are set to include a 50-fold safety margin from observed effects of radiofrequency energy exposure".[3]

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).