1. Don't Panic

The first and most important thing to do, for your sake and your cat's sake, is to stay calm. Whether your cat is nervous or not about being up in the tree, it will be able to pick up on the vibes of your mood, so if you panic and yell and act like the sky is falling, you'll only make your cat upset if it's calm, or more upset if it's already feeling skittish. Remember that the situation is probably not an emergency yet, so unless your cat is obviously injured, take a deep breath and think about your next steps.
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2. Check for predators/threats that might have chased your cat

Cats are curious, so in all likelihood your cat climbed the tree just because it felt like the thing to do, or maybe it chased some prey, like a bird or a squirrel. However, it could also be that your cat itself was the prey, and fled up the tree to get away from a neighborhood dog or some other cat bully. Do like they say in every cool war movie: Secure the perimeter. Look around and check for anything that could have frightened your cat. If you can find and remove the threat, it will help you to coax your cat back to the safety of the ground.
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3. Determine if your cat is truly stuck or caught, not just scared and stubborn

It's probable that your cat is being stubborn and won't come down because it doesn't want to, or it's frightened, but it's possible that the cat simply can't get down for some reason. It may truly be stuck, or its collar is caught on a branch, etc. Observe the cat as closely as you possibly can to see if it is stuck or struggling. If so, you won't be able to coax it down, and you should skip to a direct approach.
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4. Be patient

If your cat appears to be safe where it is, and is just relaxing and being stubborn about making a descent, the next thing for you to do is to do nothing. Take the path of least resistance and give your furry friend a couple of hours to get bored and come down on its own. Your cat may be more resourceful than you give it credit for, and could just be waiting to get down safely when it's good and ready.
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5. Use a familiar talking-to-your-cat voice to communicate with and call your cat

You'll naturally want to call to your cat and try to coax it down. Feel free to do this, but use the normal voice you use to talk to your cat every day. Again, don't panic. Don't yell angrily or demandingly. You don't want to indicate to the cat that something is wrong, and you certainly don't want to frighten it more, or give it the idea that you are a threat. That will only make the situation worse. If your cat knows certain words or phrases that you normally use to call it to you, now is the time to use them.
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6. Entice your cat with food

There's no shame in using bribery! Your cat may be hanging out high up in that tree because it's comfortable, and maybe all it needs to come down is a reason. Give it a reason! Offer its favorite food. Make sure your cat can hear you preparing the food, to signal that it's supper time. Pour the cat food into the food bowl outside so your cat can hear it clinking, rather than filling the bowl in your kitchen and bringing it outside. If your cat loves tuna, stand underneath the tree when you crack open that can. What cat could resist?
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7. Get a ladder

If your cat is truly stuck, or it's simply too frightened to come down on its own, and the patient/passive approach hasn't worked, it's time to get proactive. If you have access to an extension ladder, you can try rescuing your cat yourself. Before you start climbing, see if the cat is willing to use the ladder on its own as escape route down from the tree. If that doesn't work, and you feel comfortable taking matters into your own hands, it's time to climb. Observe all the necessary safety precautions when using the ladder. Your own safety should be your top priority. Ideally, you'll have a partner who can stay on the ground and stabilize the ladder as you climb. Go slowly, and remain calm. You don't want to frighten your cat further up the tree. If it doesn't want to come down, it probably won't let you grab it too easily even if you can reach it, so do your best to make yourself seem safe and welcoming.
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8. Use a bag or sack to carry your cat back to the ground

If you can reach the cat and it lets you grab it, congratulations! But you're not out of the woods yet. You still have to carry it down, and whether your cat likes to be held or not, this won't be a comfortable situation for either of you. Don't try to descend the ladder with the cat in your arms. Put it in a bag or a sack of some sort. Your cat might not love this, but it will keep you both much safer and your cat much easier to manage until you both have you feet back on solid ground.
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9. If all else fails, call animal control

If you don't have a ladder, don't feel safe using one, or you gave the DIY approach your best shot but weren't successful, it's time to call in the professionals. Despite the classic, small-town image of the firefighter rescuing the treed cat that many of us have in our minds, this is probably not a job for the fire department. Your first call is to your local animal control department. They're best equipped to, well, control animals. If they're unavailable, try your vet or a nearby shelter. Even if they can't help directly, they may be able to put you in touch with someone who can. If that doesn't work, go ahead and call the fire station. After all, they've got ladders, and they're professional rescuers.
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10. Comfort your cat and let it knows it’s safe

Your cat has had quite an ordeal. No matter what method ultimately gets your feline companion down from its leafy perch, make sure you give your kitty lots of loving comfort and affection to let it know it's safe.
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