Leaving your pet in a crate without toys
If you can put a comforting toy -- preferably one that smells like you -- in the carrier, it will help your pet relax while being transported. Similarly, when you get to your destination, your pet will already have something entertaining, and might associate the toy, rather than the stress of travel, with the overall experience.
Switching beds and food on the road
Since you're bringing a pet along, the convenience of only carrying on is pretty much shot. So if your pet is small enough, check its bed with your checked bags. Add to that the food your pet regularly eats. You might enjoy new cuisines when you travel, but odds are your pet isn't aspiring to recreate Parts Unknown. The combination of a familiar bed and food will give your pet a sense of familiarity on the road, and keep them calmer before the return trip.