Unplug the microwave from the electrical outlet or shut off the circuit breaker that supplies it with electrical current.
Locate the cabinet screws on the sides, back and inside the door, depending on the specific brand and model of microwave you own. You may have to do some investigation to locate all the screws.
Unscrew the screws that secure the cabinet to the microwave frame using a Phillips screwdriver. Slide off the cabinet or, in the case of a built-in, remove the outer cover of the control panel. The goal is to provide yourself with access to the area behind the screen, even if it is a small slit.
Insert the end of a crevice tool connected to the end of a shop vac hose into the area around the display panel. Move the crevice tool around and vacuum until the bugs have been removed by the suction. Reassemble the microwave and restore power.