It might not turn out crispy, but microwaved food is no less nutritious than any other kind of prepared food.
When Molecules Collide
Microwaves are low energy electromagnetic waves that have so little energy they can't trigger chemical reactions in the molecules they encounter. And as long as there's nothing in your microwave that can cause a spark, they also don't leave behind any traces.
When you heat food in the microwave, what you're actually doing is running an electrical current through the water molecules in the food. This causes the water molecules to rotate and collide, and these collisions generate friction that produces a lot of heat.
The reason microwaves are so speedy is because food is made up mostly of water. In contrast, when you use an oven or a grill, you have to wait for the food to heat from the outside in.
The Heat Is On
Consequently, the only chemical and physical changes to your microwaved food are the result of the heating process. At high temperatures, sugars and proteins might interact, and vitamins might be destroyed. The thing to keep in mind is that these changes happen regardless of the method you use to heat food.
What's more, because microwaves heat up food so quickly, some of these changes might be less drastic than in foods that are heated up over a long time.
"Is there any evidence that microwaving food alters its composition or has any detrimental effects on humans or animals?" (Scientific American)