I travel with mine all the time, in fact Im traveling cross country this weekend. As to Airports, I've never tried to take the pen needles through security, I always pack them in my suitcase, but I have no problems with the pens. I pack them in a small insulated travel bag with ice packs. I keep the pens in the original boxes that have the prescriptions on the front of them (serves 2 purposes, shows its prescription medicine and serves as insulation for the meds). The only question they ever seem to ask me is "are those ice packs" and I tell them " of course". No hassels. Seems they've gotten much better about allowing meds to travel with you as carry on. \
It wouldn't hurt to have a letter from the doctor that says you need to travel with this stuff, but I've never found that I needed it.
(PS. For convenience I often put my small travel/ice pak in my suitcase. Even if your bag gets lost temporarily, the ice packs surrounding your Byetta take DAYS to melt if they are in an insulated container.)