Hi, I have just had the same problem. I was lucky enough to get hold of some corrugated plastic, which worked really well. The pastel portrait was covered with glassine paper (tracing paper would also work), then sandwiched between backing boards, then that was sandwiched between corrugated plastic. With the plastic I had the grain going in opposite directions to give extra strength, virtually impossible to bend.
If I cant get hold of anymore plastic, I will use hard board. I hope this helps, I was able to send my artwork to America for £26, it was 16" x 16".
Good luck :-)