My hero John, came running to the kitchen to scope out the problem and found there is a mica plate mounted to the roof of the microwave and it had caught fire. He immediately started to Google microwave parts and found this is mica plate frequently needs to be replaced. Who knew?
The best price he could find for a replacement part was available at Sears for $63 USD. We have a great little domestic appliance repair shop here in Atenas, so I suggested we check with them to see if they carry mica plates. Sure enough, they carry generic mica plates that can be cut to size. Total cost ¢1500 (less than $3 USD.)
Today, John went to cut the new plate, and as luck would have it, he didn't have the right kind of saw to do the job. Off we went to the local hardware store to buy a coping saw for ¢2000 (less than $4 USD.) He was able to use the old plate as a template to cut a new one, and just like that, we are back in business with a working microwave oven.