It may seem hard to believe, but microwaving is one of the two best ways to cook veggies and retain the nutrients inside. (Steaming is the other.) Cooking methods like baking or grilling that expose foods to higher temperatures and more cooking time are much more destructive. For instance, in studies at Cornell University's division of nutritional sciences, Gertrude Armbruster and her colleagues have shown that on the whole, microwave cooking of vegetables and fruits was least destructive of vitamin C compared to other methods. (Because it is both water-soluble and heat-sensitive, vitamin C is considered a good marker for judging overall nutrient retention.)
Microwave ovens radiate electromagnetic waves (of the same frequency on which many cordless telephones operate), a band of the energy spectrum that is absorbed by water molecules inside food, which heat up. The heat then spreads to other parts of the food. Because nutrients are scarce in water content, they are likely to survive the process, says Nicholas Vacirca, a researcher in microwave engineering at Drexel University. You also needn't worry about radiation seeping out from the oven, he says: the energy is kept safely inside by a layer of mesh in the glass door.
The key to cooking vegetables in your microwave? Go easy on the water. When researchers at the University of Murcia in Spain added 10 tablespoons of water to two cups of broccoli and cooked it in a microwave, they found that the broccoli lost nearly all its nutrients. That's because whenever vegetables are immersed in cooking liquid, water-soluble nutrients such as folic acid and vitamin C leach out of the food and into the surrounding liquid. To keep the nutrients intact when microwaving, you need only a couple of tablespoons of water to cook raw vegetables; frozen ones need no extra liquid at all.