Edge-routing narrow, curved workpieces becomes a challenge without a router table. The router keeps tipping, digging the bit into your work and spoiling it. From scrapwood the same thickness as your workpiece, cut straight or curved supporting pieces about 1" wide. Arrange them around your workpiece as shown at top, and then rout away.

With the router riding on both the workpiece and the supports, you'll avoid nicked edges and chewed-up corners. Be sure to make the supports the same height as the workpiece. If you use double-faced tape to hold the workpiece in position, for instance, use it to hold your supports, too.
—Alex Polakowski, Skokie, Ill.