The device comes in a variety of forms ranging from the $39 Aries Shield ("a silicon based micro processor that ... decomposes oscillations of electromagnetic fields") to the $249 Aires Defender Utility (which "has two next generation 9 core silicon based micro processor (sic) that provide universal protection from electromagnetic smog of the broadband frequencies").
This high quality Blocsock cell phone radiation pouch is made in the UK and is something very special, it has radiation protective material that will cover the whole of the front of your phone whilst you speak and reduce your exposure to harmful cell phone radiation to the brain by 96%. If you want to use a cell phone held to the head this is the only way we know to effectively protect your brain from the two kinds of radiation emitted by your phone. Also you can use the Blocsock to protect your organs if you have to carry a phone on your person
Only 0.010 inch thick, PaperSHIELD is flexible and can be easily cut with a scissors and shaped by hand into simple or very complex shapes. High saturation and moderate permeability make this ideal for shielding weak magnets, or stronger magnets with many layers of shielding. This material is particularly suited for achieving precise levels of partial shielding as you can add exactly the right number of layers to achieve the desired result. White paper on one side can be imprinted (by you). Peel and stick adhesive on the other side permits easy and semi-permanent mounting almost anywhere. Magnets will stick to it nicely.
I love this case. However, I don't understand what happens to the radiation that must collect under the case; isn't there a burst of radiation when the case is opened? I posted this question but the answers were from people who hadn't thought of that issue; they didn't have the answer, except for one who theorized that the radiation is slowly leaking out the top, bottom, and sides. I assume the case keeps radiation off the hand that holds the case with the phone in it, which is great, but I do wonder about the stored radiation when, for example, I'm listening to a podcast with the case closed, then open it later.
Phone radiation isn’t like the radiation from, say, a nuclear meltdown. That’s what’s known as “ionizing” radiation — it’s high energy and capable of damaging your DNA, which researchers have determined leads to cancer. Phones emit a much lower energy radiation (lower even than visible light) that’s considered to be “non-ionizing.” We know non-ionizing radiation doesn’t damage DNA the way that ionizing radiation does. But the question remains whether it could still react with the body in some other way that might lead to problems from longterm exposure.
In conclusion: It is still unclear whether use of cellular technology is associated with an increased risk to develop malignant and benign tumors, but taking into account the results of recent studies, the Ministry of Health adopts the precautionary principle and follows the recommendations listed in the “Ministry of Health Recommendations” (below).

The tricky part about measuring the radiation from a cell phone is that the emission strength varies widely over time. There will be strong bursts of varying intensity, followed by quiet periods. This makes it hard to compare "apples to apples". Also, because you are measuring up close to the source, you must use a near field meter AND you must maintain the position of the meter very precisely.
However, there have been some studies that have shown that rats can develop a specific type of brain tumor, called a schwannoma, if they're subjected to prolonged radiofrequency radiation. These studies examined thousands of rats and mice, and exposed them to a variety of radiations — everything from "near-field" (which is what you get holding a phone to your ear) to "far-field" (which is what you get walking through everyone's Wi-Fi signals at Starbucks).

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.

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.
In one type of study, called a case–control study, cell phone use is compared between people with these types of tumors and people without them. In another type of study, called a cohort study, a large group of people who do not have cancer at study entry is followed over time and the rate of these tumors in people who did and didn’t use cell phones is compared. Cancer incidence data can also be analyzed over time to see if the rates of brain tumors changed in large populations during the time that cell phone use increased dramatically. These studies have not shown clear evidence of a relationship between cell phone use and cancer. However, researchers have reported some statistically significant associations for certain subgroups of people.