As long as the non microwavable mug doesn't contain any metallic rings around it or any other metal then nothing bad will usually happen to the non microwavable mug.
However the worse thing that could happen is the non microwavable mug shatters or breaks in the microwave or breaks after you take it out of the microwave.
Most coffee mugs especially the ceramic coffee mugs are safe to microwave as I've done it for years without a problem.
But if your coffee mug has any metal or stainless steel on it or around it then do not microwave it because it can create sparks in the microwave which can damage your microwave.