Choose a sandpaper grit. The higher the number, the finer the sandpaper. For example, an 80-grit paper is coarse and will leave scratches in most woods even though it is capable of removing the most material. A 220-grit sandpaper is designed for finish sanding, removing very little wood. Select something in between, such as 120-grit or 150-grit paper to start.
Wrap the paper around a block of wood that resembles the mirror image of the router cut you made. A concave edge on the block fits a round over cut. A rounded edge on the block fits into a cove profile.
Sand the routered profile using smooth strokes in the direction of the wood grain. Don’t bear down on the wood. Just allow the sandpaper to do the work. Continue sanding until the burn marks disappear.
Wrap a finer grit of sandpaper around the same blocks. Lightly run the sandpaper over the profile to remove any scratches left behind by the coarser paper.
Run the profiled edge back through the router again only if you have enough material with which to work, and if you do not make progress with the sandpaper. The cherry may still burn, but it may receive fewer burns than it did with the first pass.