Look at as many boarding places as you can, talk to the people there and find out as much as you can. The way to tell the good ones- like good breeders- is that the people will be keen to talk to you about every little detail, love talking about cats and want as much information as you can give them. They also won't mind you ringing as often as you need to to check how things are going while the cats are with them. And find somewhere you like the look of. There are some really excellent kennels around, run by people who put a lot of thought and care into the cats they board. Living alone, there are times when I have had to board the cats out occasionally and they always go to the same place, where our cats have been going for years. It's a cats-only kennels, they have good sized runs where they can comfortably put my guys in together, and they have large pens where the cats can go for a couple of hours with a lot of room to play and have a different view. The other reason I love that particular kennels, apart from the staff, is that the pens are placed in a quiet garden with a view of a lake, on which are ducks and all kinds of other local wildlife. The entertainment value for the cats is huge!
Because they've consistently gone there my guys know they go, it's fine and I always come back. It might help when you do find a place you like, to let your kitty have just one night there before you leave, to get to know the place and to set the habit that you will always come back. It IS hard, I don't like doing it and I miss them like crazy, but finding somewhere you like and you trust and helping the cats to find it routine makes it easier on all of us.
A few other things we do by habit- send some of their own toys. The kennels (if they're any good at all) will have toys in the pens, but familiar and special ones are good. Their own baskets or beds, or towels/blankets etc, or a sweater of yours that you've worn, so there's something that smells of home and comfort they can sleep on. All good kennels will feed exactly what you feed at home, to your schedule and use the same catlitter, check that in advance. And I always leave the name and phone number of my own vet, although the kennels have their own vet to attend if needed, so that their full medical records can be accessed and checked. It's the little things that keep the blood pressure down.
Much sympathy- do try not to worry though. Sometimes it is necessary, like trips to the vet. It's finding ways to make it an ok experience. In over fifteen years of contact with this kennel and many different cats, we've only had one who was unhappy during her stay, she was bordering on being semi feral, and even she ate while she was there and was completely undistressed by the experience as soon as she was home.