Styrofoam is made from and contains some bad chemicals but you can safely microwave the Styrofoam without fear of it causing any cancer or harmful effects.
The Styrofoam would have to melt to release those chemicals into the food or drink but microwaving Styrofoam cups and food containers is safe to do so and should not melt as long as you keep an eye on them and don't microwave them for too long.
Microwaving the Styrofoam for a few minutes to heat up coffee or food should not be a problem and I've done it myself several times and haven't gotten cancer or any other health problems from microwaving the Styrofoam.