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.
EWG believes that cell phone testing procedures should include cases and other accessories, whether supplied by the phone manufacturer or a third party. Since these cases and accessories have no other use and have the potential to influence the phone’s transmitting and receiving activity and the amount of radiation that a user might encounter, they fall within FCC’s authority.
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.

First, you must have a proper meter. To check for magnetic field emissions, an AC Gaussmeter will work. Most AC gaussmeters will have an internal probe. Simply position the gaussmeter on the phone. Note carefully where the meter 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 magnetic shield, and repeat.
That’s why randomized controlled trials (RCTs) often yield fairly clear answers about the effectiveness of treatments compared to other study designs. (Fun fact: Scottish doctor James Lind, a clinical trial pioneer, figured out that citrus fruits seemed to have an effect on scurvy using one of the earliest RCTs.) RCTs can also be used to study whether something, like cellphone radiation, can cause disease.
According to this sub-regulation, “a speakerphone is a device that enables use of the phone without holding it, providing that if the device is installed on the phone, the phone will be positioned in the vehicle in a stable manner that prevents it from falling”. For the regular mobile phone instrument in the vehicle, it is advisable to install an antenna outside the vehicle and not inside it, and to prefer wire connections between the phone and the speaker over use of a blue tooth.
But he cautioned that the exposure levels and durations were far greater than what people typically encounter, and thus cannot “be compared directly to the exposure that humans experience.” Moreover, the rat study examined the effects of a radio frequency associated with an early generation of cellphone technology, one that fell out of routine use years ago. Any concerns arising from the study thus would seem to apply mainly to early adopters who used those bygone devices, not to users of current models.
Jump up ^ Repacholi MH, Lerchl A, Röösli M, Sienkiewicz Z, Auvinen A, Breckenkamp J, d'Inzeo G, Elliott P, Frei P, Heinrich S, Lagroye I, Lahkola A, McCormick DL, Thomas S, Vecchia P (2012). "Systematic review of wireless phone use and brain cancer and other head tumors". Bioelectromagnetics (Systematic review). 33 (3): 187–206. doi:10.1002/bem.20716. PMID 22021071.

Participation bias, which can happen when people who are diagnosed with brain tumors are more likely than healthy people (known as controls) to enroll in a research study. Also, controls who did not or rarely used cell phones were less likely to participate in the Interphone study than controls who used cell phones regularly. For example, the Interphone study reported participation rates of 78% for meningioma patients (range among the individual studies 56–92%), 64% for glioma patients (range 36–92%), and 53% for control subjects (range 42–74%) (6).
Cordless Phones - Most homes have cordless phones. Many of these cordless phones operate within 2.4GHz 5.8 GHz. These phones are high in electromagnetic radiation particularly when they get over 2.4 GHz. At this level they are operating at the same frequency as a cell phone. We suggest using Safe Cell on your cordless phone as well as your cell phone. 

We began by getting a baseline of ambient RF in the room at the location of our testing. We then recorded a baseline of the cellphone RF while on an active call with no case. And finally, we measured the reduction in that baseline (still on the active call) using a variety of different cases and RF reducing products – all at the same set distance from the phone.
The studies are notable for their sizes. Researchers at the National Toxicology Program, a federal interagency group under the National Institutes of Health, tested 3,000 rats and mice of both sexes for two years—the largest investigation of RF radiation and cancer in rodents ever undertaken in the U.S. European investigators at the Ramazzini Institute in Italy were similarly ambitious; in their recent study they investigated RF effects in nearly 2,500 rats from the fetal stage until death.
If you would like to reproduce some or all of this content, see Reuse of NCI Information for guidance about copyright and permissions. In the case of permitted digital reproduction, please credit the National Cancer Institute as the source and link to the original NCI product using the original product's title; e.g., “Cell Phones and Cancer Risk was originally published by the National Cancer Institute.”

From the FCC website: "The FCC ID number is usually shown somewhere on the case of the phone or device. In many cases, you will have to remove the battery pack to find the number. Once you have the number proceed as follows. Go to the following Web address: www.fcc.gov/oet/ea/fccid. Once you are there... Enter the FCC ID number (in two parts as indicated: 'Grantee Code' is comprised of the first three characters, the 'Equipment Product Code' is the remainder of the FCC ID). Then click on 'Start Search.' The grant of equipment authorization for this particular ID number should appear. The highest SAR values reported in the equipment certification test data are usually included in the comments section of the grant of equipment certification."
The following charts list SAR levels for the Apple iPhone, Samsung Galaxy S, as well as 20 of the highest SAR level cellphones and 20 of the lowest SAR level cellphones. The list provides the maximum possible SAR level from the phone (many phones have differing SAR levels depending on where and how the phone is used). If your phone is not on either list, you can find the SAR level for your specific phone by checking the online FCC database.

An analysis of an "eagerly anticipated" study using rats and mice by the National Toxicology Program indicates that due such issues as the inconsistent appearances of "signals for harm" within and across species and the increased chances of false positives due to the multiplicity of tests, the positive results seen are more likely due to random chance. The full results of the study were released in February 2018.[10]
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).