This is what I do when mine goes astray.
1. Put a smally cat box outside so she can smell her own scent. If it's raining, put it under a high cover like a table.
2. Put her food outside too, -- something she really loves, something with a strong odor. If it's hot and the steam carries through the air, all the better. Do it at night when the cat won't be afraid to travel if she's scared and hiding. Also put some water out for her in case she's so spooked she doesn't recognize even you.
3. Most cats who go astray, especially housecats, become terrified when they get out and see a dog. They tend to jump a fence or something and then get stuck behind the neighbour's fence. Others may go exploring and get locked in someone's garage.
I have found my cat a couple of times this way, although the neighbours surely must have thought I was nuts:
Wait until it's perfectly quiet out, like at midnight, on a non-windy day. It can be scary going out at that time so take your car and drive it about 20 feet at a time. Roll down the windows and turn off the lights AND MOTOR. Call your cat. You don't have to call too loudly because your voice will travel far at that time of night. You will hear your cat crying if she is trapped behind a fence. If you don't, drive another 20 feet and switch EVERYTHING off again, and keep doing that until you hear her answer you when you call.
Sometimes people take other people's cats into their own houses to play with and then let them go after a few days. This is really traumatic to the owner.
Are there any kids in the area who have taken a shine to your cat? If so, ask around, or ask one child to tell all the others that the first person who finds your cat will get an immediate $20 reward. Some kids will go looking for it just for fun. You might even suggest that they ask neighbours if they will mind checking their sheds or garages. Have the reward money ready for when the cat is found because if you delay they won't look for it next time.
Most cats who stay home all day won't wander more than 5 or 6 houses away so chances are she is really close nearby. Also, if you have a neighbour who dislikes cats, make sure you spoil yours so he doesn't like food from others. Also make sure he always has something to drink so he won't drink from another source.
Check with your local animal pound, society for the prevention of cruelty to animals, or any other agency in your area that has interests in animals and ask them if they know what else you can do. Many will take your name and address in case the cat gets turned in harmed or suggest other places to call.
Look at the top of all of the trees in your neighbourhood. If your cat was frightened by something it may be up there really high, and too scared to move for a few days. To get it down easily it's nice to keep on hand a long
2x6 board with rug glued all the way down the length.
If you have a friend who has a web site, ask him if he will put that cat's picture on the web site, with a lot of key words such as your district, the colour of the cat, the size, any special markings and so on.
In my city all of the found animals' pictures are posted on the Internet by the city or the animal protection society so their owners can find them quickly. If this isn't being done in yours, you might want to suggest it.
If you have a cat door, (which is the overall the ideal solution for anyone with a cat), make sure she can get in at any time you're not home in case she has to run from her enemies.
To make sure she won't be able to get out again after she gets in, pull the door toward you on the inside of the house, and then put something like a thin cord under it, and let the door close softly over it. That way she can get in but a lot of cats won't be able to figure out how to get out again. (If she doesn't know how, don't teach her either. Mine knows she can go out only when the door pushes outward.)
When some cats are teased, played with roughly, or very unhappy they will simply run away. Some would rather starve to death than be unhappy, mistreated, or abused by others, so make sure you never do this to your cat. If the cat has ever behaved strangely around a particular member of the household, chances are that member might be abusing it when you aren't around, hard as it may be to believe.
Once your cat comes back, put a stretch collar around its neck. Leave enough room for only one finger to fit through comfortably. Make sure there is a little engraved or similar tag tied to the collar stating "REWARD: CALL (Phone number). That way, the next time she is lost you won't worry so much.
Also, if you must let your cat out, let it out very late at night so dogs won't chase it and make sure it stays in the house for at least 8 hours a day, in a comfortable place it really loves to be in, or it will become wild.