Keep pets out of the action on the day
Open doors and moving furniture are the two biggest risks on moving day. Either book a day at a boarding kennel or cattery or confine pets to one closed room with a sign on the door and their bed water and litter tray inside. Load that room last and unload it first.
Update microchip details before you move
Change the address on the microchip database and with your vet before moving day rather than after. If an animal bolts during the move an out of date chip is worse than no chip at all.
Cats need a slower introduction
Keep cats indoors for at least two weeks in the new house then let them out before a meal so hunger brings them back. Start with one room containing familiar bedding and their own scent before giving them the run of the house.
Dogs settle through routine and walks
Walk the new neighbourhood on day one. Keep feeding and walking times exactly as they were. Put down familiar bedding rather than buying everything new because the smell of the old home is reassuring.
Small animals and fish
Transport rabbits guinea pigs and birds in secure carriers in the car never in the removal van. Fish need bagging in tank water for short journeys and a full restart for longer ones so speak to an aquatics specialist if the trip is more than an hour.
In short
Confine transport by car and update the microchip. Familiar bedding and unchanged routines do the rest.