That's what I decided to do as an experiment in dehydrating liqueurs down to sugar: to see what happens when you cook Campari the fastest way possible to get all the liquid out.
I put two ounces of Campari in a silicone cupcake cup and tossed it in the microwave. After 30 seconds it boiled over. First it came to a rapid boil, then turned to a real frothy boil.
After the liquid evaporated more, the boil turned more gentle; around three and a half minutes in. But soon enough, at four minutes, came the smell of caramelizing/burning sugar.
At five minutes most of the liquid was gone, and then the sugar started blackening. The Campari turned black, puffed up, and started smoking. I had to open all the windows in my apartment to keep the fire alarm from going off.
A black crust formed where the red sugar was. After removing it from the microwave, it cooled quickly then I tried it. Surprisingly, it tastes just like a burnt marshmallow; just a little more molasses-y. There was no Campari taste to it at all.
In conclusion: That Didn't Work.