Apparently tinfoil hats may not always work as well as we hoped:

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A Faraday cage severely attenuates radio signals going in or out of it. It can be used to assure that an untrustworthy device (like a cellphone) isn’t transmitting or receiving signals when it shouldn’t be. A Faraday cage is simple in principle: it’s just a solid conductive container that completely encloses the signal source, such that the RF voltage differential between any two points on the cage is always zero. But actually constructing one that works well in practice can be challenging. Any opening can create a junction that acts as an RF feed and dramatically reduces the effective attenuation.

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What does that mean for us? Conservatively, as a practical matter, 80 or 90 dB of attenuation is plenty, unless your phone is within a few feet of a cell tower antenna (which is an unsafe place for your body to be in any case). So we want our Faraday pouch to provide at least that much attenuation at the frequencies of concern.

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“Wrap it in tin foil” is perhaps the most common advice found on the Internet for making a makeshift Faraday cage. In my experiments, I found I could sometimes achieve approximately 90 dB attenuation by carefully wrapping the generator in foil and double folding the seams on all sides, which is quite good (comparable to commercial pouches). Unfortunately the results were extremely inconsistent and difficult to replicate. The same technique that produced 90 dB attenuation in one test would produce only 50 dB the next time, with no visually obvious differences. It is extremely difficult to reliably obtain a good RF seam, at least with the kitchen-grade foil I used.

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Testing Phone-Sized Faraday Bags
Reliable tools for the modern paranoid.
mattblaze.org