I had forgotten about Rescue Remedy. I think I even have some around.

I have gotten lots of good suggestions, I'll have to start with not petting him to try to calm him (it didn't occur to me that it would encourage his behavior). I do have some doggie downers, but I only like to use them in extreme cases as they seem to affect his coordination. We're fortunate in that he's not a barker--he paces, pants and shakes but nothing that will disturb the neighbors.