When I drove by the place where that guy lives - the politician who called me a liar, I realized I still wasn't over it. But didn't want to spend energy on the issue or him. I wanted to let it go in a healthy way. So I said aloud, "I still have issues with you, but I wish you peace." My energy settled right down.
When I had an argument with a family member I thought, "I don't know how to make this better, but I wish you peace."
When I saw a TV personality make an ass out of himself and his great country, I said "I don't like your worldview, but I wish you peace."
The wish for peace must be genuine. None of that fake-it-til-you-make-it stuff. If I can't dredge up an ounce of genuine tenderness towards them, then all it does is keep the discord alive.
Wishing someone peace may not resolve the problem, but the weight of authentic compassion, love, kindness goes deeper and reaches farther than any issue I may have with them. And it helps me let it go.