@amber100,
After 6 months with no contact, you will probably have to accept rejection. Hopefully it is getting easier for you to move on with time.
That being said, if you send him one email (or something equivalent) after six months, I don't think that is inappropriate.
You can say you miss him and ask if he would like to see you again. If an ex-girlfriend got back in touch with me after six months, I would be OK with that. If you do this, don't apologize or beg. Just say "Hi what's up", you can tell him you are thinking about him and that you wonder how he is and that you miss him and would like to see him again, but nothing more.
Of course you are taking a bit of an emotional risk. He could ignore you (and you should respect that if he does). He could say he doesn't want to talk (which you should also respect). He could say he wants to see you again (which you need to accept might mean your feelings get hurt again). I might say that I wouldn't mind a friendship but not a relationship (which you would have to accept).
As long as you are able to accept whatever happens, and that you realize that you probably won't be getting back together with this person, it doesn't hurt to reach out after 6 months. If an ex-girlfriend sent me a respectful message after 6 months, I would certainly respond considerately, and I may even accept at least some level of friendship.