My cat Max has been missing for about six weeks, and I have been very depressed, trying to search for him. I also didn’t know if the way I was searching for him was the smartest way to do it. A friend of mine introduced me to Mark, a guy who lost his cat but found her a few months later. He used an approach I had never thought of and wanted to share it. See Mark’s video here: https://www.youtube.com/watch?v=_-qnmIEUXaE&t=64s
According to Mark, sometimes cats get triggered into a self-preservation/quasi-feral mode. If they get attacked by another cat, say, they can start hiding during the days. They could even be hiding near their house, but you probably would not see them.
So Mark started monitoring his property with little cameras. He was even kind enough to lend me a couple. You set up the cameras in places the cat might slink around or are a little hidden. Nowadays these Internet cameras can detect motion and record it, so you learn what cats are hanging out around your house. If you see your missing cat, great.
If not, then you should try trapping. He was also kind enough to lend me a couple traps, and I have one of my own. If the cat is in survival mode they may not come when you call their name, so you have to buy the stinkiest and smelliest food they love, and use it as bait in the traps. Again, you want to put the traps near places a cat would feel safe. Camouflage the trap with a blanket or some thing that makes it look less like a trap, like a couple old blankets perhaps. You can also put catnip on the trigger plate inside, which will encourage them to push it.
If you do try trapping, it’s extremely important that you regularly check the traps! you can even use your Internet cameras to monitor the traps. But you do have to be vigilant because you are likely to trap other animals and you have to release them.
I have used these Wyze cameras in the past. They're reliable, have a lot of features (including night vision) and are relatively cheap. They make an outdoor one that is battery powered so you don't have to run power to it: https://wyze.com/wyze-cam-outdoor.html
More info coming later. If you want to help, you can download the Shadow lost pets app and screen photos of shelter cats with me. I'm pretty impressed with the app so far.