I did a project once where I needed to block RF interference from a battery-powered Raspberry Pi board. I thought back to physics classes and Faraday cages when we learned that no electric fields can come in or out, so I went and put the board into a metal box thinking it would completely block all RF. Boy was I wrong. The box was only enough to attenuate about -10 or -15dB of the WiFi signal! I figured the box had seams so it was behaving as a repeater from outside to inside. I wonder if a perfect seamless box would have done better.
You forgot an important detail from your physics classes: the electric field inside a Faraday cage is only zero when it's exposed to static electric fields. Changing electric fields, like radio waves, can pass through, although they'll be attenuated.
Also, if you place an electric charge inside a Faraday cage, it will cause an electric field outside the cage, and the electric field inside the cage will still be zero.
Seamless might have helped. Seams can act as slot radiators.
In plasma deposition chambers I've built, getting continuous electrical contact all the way around mechanical access ports was essential to keep microwave power from getting out of the box.
