Some nutrients break down when they're exposed to heat, whether it is from a microwave or a regular oven. Vitamin C is perhaps the clearest example. But because microwave cooking times are shorter, cooking with a microwave does a better job of preserving vitamin C and other nutrients that break down when heated.
As far as vegetables go, cooking them in water robs them of some of their nutritional value because the nutrients leach out into the cooking water. For example, boiled broccoli loses glucosinolate, the sulfur-containing compound that may give the vegetable its cancer-fighting properties (as well as the taste that many find distinctive and some find disgusting). Is steaming vegetables — even microwave steaming — better? In some respects, yes. For example, steamed broccoli holds on to more glucosinolate than boiled or fried broccoli.
The cooking method that best retains nutrients is one that cooks quickly, heats food for the shortest amount of time, and uses as little liquid as possible. Microwaving meets those criteria. Using the microwave with a small amount of water essentially steams food from the inside out. That keeps in more vitamins and minerals than almost any other cooking method and shows microwave food can indeed be healthy.
https://www.health.harvard.edu/staying-healthy/microwave-cooking-and-nutrition
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