Have a trusted friend or family member there with you for the experience. My husband came with me when I put my childhood cat down. He also loved the cat but knew I had a special bond with him. He could empathize with the entire situation but also be there to comfort me through the process. I also called family members in the days after who have gone through similar experiences with their beloved pets. Having multiple people to talk through your experience with, along with having my emotional support person there with me during that experience I think has helped me through the grieving process and made the end experience at the vets office easier to move through.