Mylar by itself is not conductive, and therefore cannot be a Faraday cage. Some of the bags used to protect electronics have metal shielding in the Mylar. Those may work.

Tealights and mylar. At work we call this scope creep. But at the shooting range, that term means something completely different, and disturbing.

There's always the microwave theory -- good at keeping energy in, thus good at keeping energy out, too. Besides, if we get hit with an EMP, it's not like you will be needing the microwave to make popcorn.