Interesting choice Jim. I'd be interested in your dislike for tubes.
If I send anything that absolutely must not get damaged (no finger marks or corner dents) I would always choose a thick walled tube. *Very* loosely rolled. Just make sure the art is covered in acid free tissue paper, front and back, with no chance for the art to shift length ways in the tube (foam or polystyrene plug).
If you want to send art on Bristol board or art that can't be rolled for any reason (painted, heavy paper sort), then I mount it between two sheets of hardboard/thick card like Jim said, but then boxed with at least 1cm space (foam/bubblewrap/chip filled) on all sides. No matter how thick the card is, if it gets bent your art is fugged. Air space surround is essential. Always make sure your backing boards are bigger than the art (not the exact same size) and make sure it can't shift so a corner wont stick out.
The amount of effort is of course dependant on how valuable you think it is!