How to best keep a 15yr old cat calm at the vet

My cat Buddy is 15 years old and hasn't been to the vet in years. This is because it would stress him out so much that he would stop eating and drinking for days and give himself bald spots from overgrooming. My mom and dad decided it was in his best interest to stop going regularly because he was always perfectly healthy. Recently he has started to have trouble with getting to the litter box in time and has been peeing everywhere. We already tested his blood sugar and he doesn't have diabetes, but now we have to take him to the vet for a uti check. I'm worried about him based on his struggles in the past and don't know what all i can do to try and keep the experience as calm as possible for him. With his age I'm worried about him causing himself problems by working himself up to much. My other cat Lucky has anxiety meds and we were debating giving him one to help, but we dont know if it will mess with the results. Any tips to help keep him as calm as I can that won't affect the uti results?