For year I had always used sandpaper to remover burn marks. However, this process is very slow and it is very easy to round a crisp edge with sandpaper.
I've found using a hand plane to be the fastest and best way of removing burn marks. In less time than it takes for me to find my sandpaper I can remover the burn marks using my hand No. 4 smooth plane. Just about any plane will work for the job but smaller planes are ideally suited because they are just easier to use and are easier to keep close at hand. For many people a block plane would be ideal. It is really just a matter of preference. Whichever plane you choose, it will just take a few very light passes and all of the burn marks will be removed. While it isn't a replacement for turning up your saw or sharpening your router bits, it works great on woods like cherry that have a tendency to burn.