Quick Answer: You should not microwave melamine dishware. According to the FDA, melamine is not approved for microwave heating, as you'll discover.
First, let's find out what melamine is...
What Is Melamine?
Different Types of Melamine Dinnerware
How Do You Know If Plastic Dinnerware Is Microwave Safe or Not?
Labels on Plastic to Be Aware Of
The label you want to look for on microwavable dinnerware is "microwave safe." It's also possible that you could find a label that refers to the opposite, that the item is not microwave-safe.
These labels should be highly visible and easy to find on or near the bottom of the product. If you don't find one, you can contact the manufacturer to confirm.