Flip the coin, try to ignore the anxiety for just a few minutes, and start to do stuff that you can only do when you're alone (for a longer period of time) -- and do them! Dance around naked, sing along to your favourite tune, make faces to the livingroom mirror, turn the volume to max on the stereo! Go crazy, go crazy in a way you couldn't when you aren't alone. Exaggerate your panic until they're funny, nobody's there to see it!
Ok, so not this isn't all realistic for everyone, but this is what I do -- now that my girlfriend's abroad for a longer while. :D