Would you then suggest unplugging the microwave, thereby making sure you aren’t connected to the house’s ground circuit? Serious question.
It does not matter if the Faraday cage is grounded or not. If you are doing a double-wall shield, then grounding the outer one stops static charges, but the inner one floats.
I’m not sure that an unpowered device small enough to fit in a microwave would be impacted by an EMP pulse, unless it had a long antenna on it.