Light both ends of one fuse and one end of the second fuse. When the the first fuse burns out, light the remaining end of the second fuse. This is where we begin measuring our 15 minutes. Once the fuse is out, we have measured exactly fifteen minutes.

Why does this work? If you light both ends of an hour-long fuse, they both ends will meet each other after half an hour. This is because they each burn for the same amount of time, and that time needs to add to an hour. If you also burn one end of the other fuse at the same time, after half an hour, you have a fuse of half-hour length. Lighting the other end, the fuse will burn for exactly half the total fuse time: 15 minutes.