Wet a soft sponge and wipe down the surfaces of the microwave. Allow the microwave to dry.
Apply some kitchen cleaner to the sponge or use cleaning wipes to wipe the microwave surface clean. Allow to dry.
Place a small amount of car wax (ideally one labeled for dark colors) to the scratches.
Use a clean soft cloth to buff out the scratches. Work the wax into the scratches using a circular motion. Repeat as needed until scratches are removed or minimized.
Wipe off excess wax with a clean towel or cloth.