I'll also support not holding them so tight, to avoid (not prevent, just avoid) pieces flying off into space.
To avoid scratching or otherwise damaging a piece, though, coating them with that plastic coating or similar product is a good idea. I use masking tape sometimes for that purpose. I'll wrap the jaws of alligator clamps with masking tape, too, for the same purpose.
If you don't mind scratching the piece, then Mike's technique of gluing fine-grit sandpaper to the inside of the tips is very good, too.
There are also plastic tweezers, too.