I am assuming that a microwave oven is a Faraday cage. Since it keeps
the radiation trapped, bouncing around inside to heat up the food
instead of you. I am betting you would loose signal on a cell phone
completley if it were placed inside of a microwave with the door
closed. This should work even with the oven unplugged from the wall
outlet, which then would be ungrounded.

The electric field inside a Faraday cage is zero, regardless of what
the outside is doing or is connected to. But the reverse is also true.
The charges that are built up from components inside of the Faraday
cage are trapped to bounce around like the radiation inside of a
microwave. So that makes me think it needs to be grounded. On the
other hand, if the shell of a microwave is grounded. Then what keeps
the radiation inside from going to ground instead of bouncing around
and cooking your food?