Many dogs and cats get anxious when in unfamiliar, stressful  situations. If your pet tends to get anxious, put one of your unwashed  t-shirts into the carrier. Smelling your scent will give them some  comfort. If you are thinking about giving your pet tranquilizers before the flight, thoroughly research before giving your pet anything. 

While  many online sources say it is okay to give your pet tranquilizers  during a flight, the internet is not always a reliable place for medical  advice. Even your vet might not have all the answers! Pet Relocation says that it is dangerous to tranquilize your pet while flying, because  the altitude may increase the risk of heart and respiratory problems.  It is largely unknown what effects high altitudes can have on sedated  animals and, furthermore, every animal reacts differently to sedatives. 

There  are natyellural alternatives if you really feel that your pet would benefit  from something to calm them down while in the cargo. Rescue remedy is a well-known natural sedative that calms animals when they are  stressed, but does not knock them out like perscribed tranquilizers. PassPawt suggests other natural methods for calming dogs for travel, including smelling essential oils. 

Cats  require different remedies to dogs, with catnip being the most  well-known natural alternative to sedatives (but there are also many other natural remedies).  Only 50% of cats respond to catnip, so it is highly recommended to test  these remedies on your cat before flying. This goes for dogs too – you  should know how your pet will react to herbal treatments, and you should  give the treatment to your pet a few times before flying. Your pet  should be as safe and calm as possible.