When a frightened cat will not come to you, a covered, baited, closely watched box trap can bring it home safely. Here is the method.
The short answer
To catch a lost cat with a humane trap, borrow a box trap from a shelter or rescue, set it on flat ground where your cat has been seen, put strong-smelling food at the far end, and watch it from a distance. Never leave a trap unattended. When the cat is inside, cover the whole trap with a towel to calm it, carry it level to a quiet room and open it into a closed space. Use a trap only once you know your cat is in the area and will not come to you. Ask your local animal control if any rules apply first.
When a trap makes sense
A trap is not the first step. Most cats are found by looking nearby, and some will come to food or a familiar voice. Consider a trap when you have seen your cat or have a camera image, it will not let you approach, and it keeps returning to one place. Food going missing is not proof, because raccoons and opossums eat cat food too. The research is limited: in a study of 1,210 missing cats, trapping did not show a clear link with cats being found alive, so think of it as a tool for specific situations, not a guaranteed fix.
Where to get a trap
Ask your local animal control, shelter or cat rescue first. Many lend out or rent traps, and some have volunteers who will set them with you, since they are used for trap-neuter-return work. Ask how the door mechanism works and whether anyone can help at the time. Alley Cat Allies recommends using only a humane box trap or drop trap. If you buy one, look for a trap made for cats, and consider one with front and back doors, which makes it easier to transfer the cat. Do not use a homemade contraption or a snare of any kind.
Check the rules and the land
Before you set a trap, check with animal control or the property owner. Do not put one on anyone else’s land without permission. Rules on trapping vary by place. Say that you are trying to recover your own pet and ask if there is anything you need to do. Tell the neighbors, too, so nobody springs the trap or releases your cat. A clear note taped nearby, saying trap to catch a lost pet and giving your number, helps.
How to set it
Put the trap on flat, stable ground, as a wobble can stop the door from working and may spook the cat. Choose a quiet, hidden spot, close to where your cat has been seen, such as along a fence or under a deck. Alley Cat Allies suggests about a tablespoon of smelly food such as tuna in oil or sardines at the back of the trap, so the cat has to step on the trigger plate, with some juice drizzled toward the entrance. Line the bottom with a thin layer of newspaper if your cat is wary of walking on wire. Test the door a few times before you bait it. Secure the bait so it cannot be pulled through the wires.
Watch it, always
Alley Cat Allies is firm that traps should never be left unattended. Stay somewhere you can see the trap but far enough away that the cat feels safe, such as your car or a window, and check frequently from a distance. Heat and cold are real dangers, and a trapped animal cannot escape either, so never set one in full sun or in freezing conditions. A trail camera linked to your phone can help, but it does not replace you being nearby. Do not leave it set overnight unless you are watching it. Close the trap when you go to bed if you cannot keep checking.
When something is inside
Walk over slowly and speak quietly. If it is your cat, immediately cover the whole trap with a large towel or sheet, which helps calm a frightened animal. Do not open the trap outdoors, however much you want to hold your cat. Carry it level with both hands, and put it in a quiet, warm room with the door closed. If you caught wildlife or a cat that is not yours, step back. Do not handle a raccoon, a skunk or any animal you are unsure about, and call animal control for advice.
Getting your cat out safely
Place the trap in a small room such as a bathroom with the window shut, cover the sides and allow your cat to settle first. Offer food and water once it is calm. Some traps have a back door, which makes it easy to transfer the cat to a carrier. Your vet can check the cat for injuries, worms or fleas and can scan its microchip. Book a visit soon, and let the vet know how long your cat was missing.
After the catch
Take down the traps and the posters, thank the neighbors and tell the shelter your cat is home. Update any reports you made with the microchip company. Return the borrowed trap clean. Keep your cat fully inside for a while, because a cat that has just had a stressful experience may be startled and try to bolt from the same door.
Sources
Alley Cat Allies, steps for a successful trapping day: alleycat.org/community-cat-care/steps-for-a-successful-trapping-day. Huang et al., Animals, 2018: pmc.ncbi.nlm.nih.gov/articles/PMC5789300.