You can microwave plastic cups but don't microwave the plastic cup longer than a few minutes at a time or it may melt.
Plastic mugs can be microwaved but they should only be microwaved for 1 minute at a time and a maximum of 2 minutes or they could possibly melt.
You can microwave plastic coffee mugs for at least 1 minute or 2 minutes at most.
Microwave the plastic coffee mug for 1 minute and then if needed microwave the coffee mug another minute until the coffee or drink is reheated enough.
Just be sure the plastic coffee mug has no metal screws or anything on it.
Most plastic coffee mugs however are free of any metal but I've had a few that did have a few screws for the handle.
Ceramic coffee mugs can also be microwaved but stainless steel coffee mugs cannot be microwaved as they will spark and cause a fire or damage to the microwave.