I've read a lot of "I lost my (cat, dog) and I want it to return." Here is a way of calling them back to you and protecting them at the same time.
Using a baking dough recipe (see the internet there are plenty of not edible baking dough recipe) and use small cookie cutters or shape with a crafting tool a symbol of that animal (cat, dog, cow, horse - whatever) - be sure you have two that look as alike as you can make them. Use a skewer to poke a hole in the top of the little talisman. Then bake the dough. I have found that making sure the dough is rolled out well, so there are no air bubbles is important and making sure the figure isn't to unwieldy is important.
Take permanent colored markers and mark the figures with symbols of protection and a symbol that will represent you. Make sure both symbols are marked similarly. In sacred space, charge the amulet with your energy focusing on the health and safety of the animal.
Keep one on, in or near your altar (be sure to protect it so it doesn't get broken) and attach one to the animals collar.
If the animal gets lost, you can use your talisman in a simple ritual to visualize the return of your animal.
This is also doable with one of those charms you can buy at the pet stores in those vending machines? Before getting one, write a simple spell of protection and safety and then put your name and number on one side and the spell on the other. Or the spell on one charm and your name and number on the other. Make a duplicate of the spell charm.
Take it home and charge the charms as mentioned above and utilize them in the same way as the dough made ones.
I might point out that you can also have your animal tagged with a microchip. My service animal, Alice has the microchip and a charm she wears. Sometimes common sense is the best prevention of disaster.
One other point is this same technique can be used to create charms for your lovers, friends and families and I have been part of a group that makes small talisman and sends them to service men at war in the middle east. Kind of like a St Christopher metal for pagan service persons.