Several (much-quoted) studies have suggested that microwaving foods reduces their nutritional value, but many of these have been accused of comparing the cooking methods unscientifically - it is very easy to overcook or to cook too quickly with a microwave oven - and many other pieces of research carried out during the 1980s found that, when microwave ovens were used at lower power, they reduced the nutritional value of foods less than conventional cooking methods:

Eight whole legumes (French beans, broad beans, lentils, Bengal gram, field beans, cowpea, green gram and horse gram) were cooked in either a microwave oven or in a pressure cooker. Neither method caused any significant reduction in iron, calcium or phosphorous. Both cooking methods reduced the thiamine contents of the foods by approximately the same amount. Pressure cooking reduced dietary fibre content slightly more than microwaving. Pressure cooking improved in vitro starch and protein digestibility slightly more than microwaving [1]

Both heating milk in a microwave and heating milk by immersing a container of milk in hot water reduced its ionic calcium content by approximately 90%. In both cases, the temperature of the milk was brought to 75oC and to 85oC then allowed to cool to room temperature.
The ionic calcium content of the microwaved milk was restored to normal by storing it at 20oC for 24 hours.
Microwaving lengthened both the coagulation and curd formation rate of the milk. [2]

Neither boiling, grilling, frying nor microwaving reduced the level of omega-3 essential fatty acids in herring [3]