Cats are notoriously difficult to transport. Unlike dog which are easier to teach, cats are fiercely independent and hard to train. They are also quick to get anxiety when taken into unfamiliar territory. They get restless and pee all over the place. Their stomach may turn causing them to heave or leave solid waste on their cage. They will probably make a lot of noise as they try to claw their way out of the situation. The cat transport company will do everything in its power to make the trip hassle-free. You as the owner can do extra preparation to ensure a smooth ride.
Familiarity
One of the reasons why cats do not like traveling is that they are placed inside a box that is unfamiliar to them. They panic at all the strange sensations that come with this including claustrophobia, the smells, and so on. Reduce this anxiety by getting the box that will be used in advance. Put it somewhere in the house where the cat will encounter is a great deal like the living room. It is pass the box back and forth and finally try to get inside once it gets curious. Let it go there by itself and spend time inside to get comfortable with the likely conditions during transport.
Food
If the cat is not taking well to the box, then try enticing it by placing familiar items inside. Get its favorite toys, rags, and any other object that it is known to like. These might be enough to make the cat go inside and stay there for a while. Its smell will eventually permeate the container until it becomes a second home. Another method you can try is to place great food inside. Perhaps you can serve some meals in the box and let the smell entice the cat to enter without any additional prompting. In time, it will do so even without stimuli.
Fasting
On the day of the transport, be sure to get the cat fasted for a reasonable period. This will prevent it from peeing or pooping all over the place if it ever gets anxious. Such would just make the box unhygienic throughout a flight and possibly cause infections. Keeping things clean is also a courtesy to the carrier which hosts other animals and cargo which should also be protected. Stop providing food several hours before the flight. Water may be given up to two hours before take-off, in case the cat is still in your possession. Encourage waste excretion prior to the flight.