Turtles don't have passports. What country are you going to? If it's one in Europe, I think the importation of RES is extremely difficult (by now they could be banned). My RES came back to the U.S. with me from Japan. I basically did two things: One, I checked with the Japanese authorities to make sure he'd be allowed out (it depended on which CITIES list he was on, and RES aren't threatened, so they didn't care). To get him into the U.S., I contacted the U.S Fish & Wildlife Service and was sent a form to fill out (his traveling papers and probably the "passport" you may be thinking about).
I suggest, if you're going to to this above board, that you start with the USFW service to find out about taking him out. Then check with the authorities of the country you're going to. (If you return with your turtle, you'll have to go through the red tape all over again.)
The airline is a separate issue. Most don't allow reptiles on board and allowing him into be put cargo is chancy--he could freeze if the cargo area isn't heated adequately. This happened to someone who was bringing his turts to Canada from Asia. He lost multiple turts and the airline could not be held responsible for it.

"You become responsible, forever, for what you have tamed." -Antoine de Saint Exupery-