I’ve flown with two (and a family member; each person can only carry one) and it was pretty uneventful. My vet did give a small dose of ace to give before we boarded. One was restless during takeoff but fine afterwards, the other was fine the whole time. I had a hard carried for one and a duffel-bag type for the other and definitely preferred the latter-much easier to carry over my shoulder.
Definitely use a harness with plastic fittings for security-it gives you something to grab onto! Also, make sure you have a way to offer water. I had a cup with me and offered water several times throughout the whole process. They did check my rabies and health cert, so make sure you have them. Health cert must be within a certain number of days (I think it was either 7 or 10).