Those who are hypercritical about microwave heating kills nutrients here is some clue that I know for fact. Microwave cooked food neither cause cancer nor destroy the nutrients. Every proteins or nutrients after heating gets denatured either microwaving or direct heating which does not effect for nutrients. In some cases like breast milk research has shown some damage on immune cells.

Second, microwave heats those which have water molecules inside it so you can't heat solid hard dry food (you need to put water in it). The way it works is by resonating wave that comes from microwave itself (usually longer even radio waves which are not harmful) inside the water molecules. Then water molecules vibrates in very high frequency equal to the microwave frequency producing heat that make your food hot.

However it is better to microwave foods in Clay (clay) or BPA free plastics. Usually plastics which are not BPA free can cause cancer. During the heating plastic will realse BPA and that mixed in too the food . So either use clay or BPA free plastic to microwave your foods.