We recently traveled with our cats across the country. They were under the seats in front of us. The vet gave us gabapentin to give to them, starting the night before, so that they were just calm and easy to handle throughout the whole airport and airplane experience. By the time we got to our hotel that night, we were, all of us, exhausted, but the cats had traveled calmly and safely.
A few tips: Tfhe vet emailed us their fit to fly paperwork. I printed it out and kept it in my handbag, along with hard copies of our boarding passes, etc. The airline never asked to see the cats' paperwork, but I felt much more at ease knowing that I had it handy, and did not have to scroll through my phone looking for the email. My husband took the cats through secondary screening at TSA. Basically, he said they took him to a small room, where he removed each cat from the carrier (one by one) so that the carriers could be screened for explosives, etc. A TSA agent happily played with the cat that my husband was holding while the other agent checked the carrier. It was all done quickly and the agents were very nice about it. I waited outside with the rest of our things (coats, my handbag, etc.). Like Jenn, we made sure to have a familiar toy and a small blanket that smelled like us in each carrier. It helped, I think. We went to the family bathroom to offer them water from bottled water and collapsible bowls we had before the flight. We did the same upon arrival.