I just flew to England and back with a guitar — not a Martin or anything comperable, mind you, but still an axe I would hate to lose — in a gig bag. I checked ahead of time and was assured I could take in on as carry-on luggage. The only limit was a 46-inch length restriction, which was exactly right for the guitar.
On two of the legs (Detroit - Newark and Gatwick - Newark) there was no room in the overhead, so a stewardess let me put it in the closet between 1st class and coach. No harm to it, but I was the only one who touched it.
Hope your travels go as well.