Or you could make something like those Rockler clamps. Drill holes in a piece of stock to fit 3/8" dowels, then cut in half so each half has two channels. Drill a hole for a nut and thumbscrew to apply pressure.
Or replace the jaws of a plastic spring clamp with jaws with channels for 3/8" dowel. The channels don’t even have to be round. They could be v-channels.