Cats that do the best staying in a cattery are usually those that have been well socialised. This is the process of acclimating a cat to other humans. A well-socialised kitty is likely to be affectionate with the majority of people, or will at least refrain from running away whenever someone new enters your home. A poorly-socialised cat is often timid and distrustful, and they will often become extremely scared, and possibly aggressive, in a cattery.
Your cat's socialisation will depend on many factors, particularly how it was raised as a kitten. Additionally, certain breeds, such as the Russian Blue, tend to be wary of strangers. However, even a well-socialised cat can struggle if they live with only one person, and that will make entering a cattery that much harder. If this applies to your cat, take these steps to make sure that your cat is well socialised.
1. Slowly Introduce Other People
Cats generally choose one person to be their special human, even if they're living with a large family. However, there's a difference between having a favourite and only tolerating one person. In some cases, a cat will even refuse food from someone new. This is why it's important to introduce them to strangers.
Make sure you have people over regularly, but don't force interactions. If your cat hides initially, just wait. They will usually come back when they know the situation is safe. Let your guests know to keep their voices quiet and calm, and make sure they don't try to handle your cat before it knows them.
2. Let Other People Feed Them
It's no secret that cats tend to bond with people who feed them, so having strangers give your cat food is a good way to let them know that other humans are trustworthy. However, as stated above, some cats will refuse, even when they come to accept the presence of other people.
If this is the case, try starting slow by having your guests offer small treats instead of the main meal of the day. You might also consider saving special meals, like some sliced chicken, for newcomers to feed to your cat.
3. Leave Them with Other People
By the time your cat is regularly meeting with other people and accepting food from them without seeming concerned or anxious, they are already well on the way towards proper socialisation. The final test is to put up with other people when you aren't there.
Once your cat gets acclimatised, pick out a certain visitor you know they are comfortable with, then ask them to spend the night when you are away for a day. The cat will not have you, but they will feel safe in their own territory. If they take this change well, try having that person take your cat for a night in their own home. The cat will be in a new environment, but will also be with a person that they know and trust.
By the end of this process, your cat should be adjusted to being with other people and away from their homes. Entering a cattery isn't going to be quite the same, but they'll be far more mentally prepared for the task.