Breaking up with someone you've been with for sixteen years would definitely feel like a big loss. You can make it clear you did not cheat on him in an email, text, or in-person. You do not have to get into it with his new girlfriend. That might just cause more stress for you. But if you found yourself saying horrible things or did anything particularly bad to him when you were together, you can also apologize for it, even if it doesn't lead to you two being back together. At least this will help you feel better.
Unfortunately, long-term couples and married people have ugly fights. It is a consequence of emotions being built up and being in close proximity to someone. If his heart is with someone else, there is not much you can do to change it. Be decent to him when he is around. Be easy to talk to. He will find it more pleasant to have you in his life in some fashion this way. You can also give yourself a mini makeover. This could help give you a boost and perhaps make his head turn when he sees you too.
Despite living in a fast-paced society, it is not odd to miss somebody's presence for many years. It hurts when we see someone we love with someone else. All hope might not be lost either.