Apparently almost any polar compound will be heated by a commercial microwave oven. Sugar gets warm - salt doesn't. There are some plastics that get hot in a microwave oven. We've got a bunch of distorted tupperware containers as a result of heating leftovers in the microwave. Anything that contains water molecules - wood, many ceramics, popping corn etc will be affected, but metals are heated as well - perhaps by a different mechanism?
Anyway, I did cook a piece of granite for several minutes and it failed to show any effect - didn't even get warm. It would be interesting to determine the "law" that governs how a substance will behave when subjected to microwaves.