Yes, sublimation mugs are microwave safe. Sublimation is the process of going from a solid to a gas, so when you microwave a sublimated mug, the molecules of the mug expand and rise into the air.  However, because the molecules are still stuck together, they reform into a solid when they hit the surface of the cup. That's why you'll often see condensation on the outside of a sublimated mug after microwaving it - it's just water vapor that's condensed on the surface of the cup. When you're finished microwaving your sublimated mug, let it cool down before handling it.