Keep your cats blankets, toys, beds, food, and water out until moving day to keep them in their natural state for as long as possible. Pack the cats belongings, extra food, and water in a set aside empty box the day of the move. This helps to put their nerves at ease for as long as possible. But before the move make sure to take your cat to the veterinarian and make sure that your vet issues any vaccinations or procedures needed, so that you have a fresh start for your move and updated records. Get copies of the updated records and keep them accessible while in transit. When you begin to pack your belongings, the best non-threatening way, is to pack and empty one room at a time. After one is completed place your cat inside the room along with its travel crate, bedding, toys, food, and water. This process allows your cat to feel accustomed to its crate and its new room/home throughout the packing process. Keep your cats blankets, toys, beds, food, and water out until moving day to keep them in their natural state for as long as possible. Pack the cats belongings, extra food, and water in a set aside empty box the day of the move. This helps to put their nerves at ease for as long as possible. But before the move make sure to take your cat to the veterinarian and make sure that your vet issues any vaccinations or procedures needed, so that you have a fresh start for your move and updated records. Get copies of the updated records and keep them accessible while in transit. When you begin to pack your belongings, the best non-threatening way, is to pack and empty one room at a time. After one is completed place your cat inside the room along with its travel crate, bedding, toys, food, and water. This process allows your cat to feel accustomed to its crate and its new room/home throughout the packing process.
I echo Marie's comments: to be 100% sure your kitties are safe, get them out of the house or apt. when moving, on BOTH ends of the move, until everything is quiet and settled. BTW, I tried harnesses on the two newest when they were both less than 2 yrs old, and (1) they both reacted as if their back was broken (oh, mom, this harness is so heaaavvvyyyy), and (2) one managed to get out of her "escape-proof" harness during the drive while under the driver's seat (where she'd scooted at the first opp prior to going into crate) ... at least she chose to stay there for the first 1200 miles, rather than get out and moving around the car.
When I've had the opp, I've used a screened patio or "Florida room" to isolate the girls while moving in or out, vs. taking to board at the vet's.
And, as Marie also recommends: catnip party and their favorite treats ASAP in the new place ... leave closet doors open, etc. Funny enough, despite the cranky reputation of Siamese, my two Sia's did much better with moving than did my tiger stripe. Actually seemed curious rather than shell-shocked when released in their new environment.
Oh, and even if you don't usually keep a collar on your cat(s) -- I don't -- put one on while moving. Only one of my girls is "chipped," but I alerted the vet where I was moving from that we'd be on the road, and how to reach me if a call came in about either cat.
P.S. I keep in my wallet a card that has, in addition to my own emergency contact info, my vet's number and that of my pet-sitter. I don't often have the cats in the car (except for trips to vet), but my little dog often is with me; in case I'm incapacitated, I want emergency folks to know who can be called to either take care of my animals or provide medical services to them.
I made the experience that placing the carrier with its front grill towards the front window of the car quietens my cat because she can look outside and relate the car's movements to her gravitational feelings - much the same as humans using a ferry would feel.
Once the cats are in your new home, leave them some room to hide while they're adjusting: under the bed, open closets. Cats hate new places. Familiar things -- their beds, toys -- should be available to them as soon as possible. Oh -- and a catnip party as soon as you've unpacked is a great way to make them feel better about their new surroundings!