Consiglio: Make sure you’re a little uncomfortable when you apologize. If you feel too good about it out-of-the-gate it may be actually be self-serving and come off as insincere.

I have no professional experience or skills in apologizing. I just screw up a lot. I've learned that when I feel warm and fuzzy before the apology it's not received that well. But when I take a moment to be vulnerable and remember exactly what I did wrong the apology goes much better.
I think it grounds me and reminds me that I'm not through it yet. I haven't received the forgiveness yet. Even if it's something super small and a genuine apology seems like over-kill – it's never over-kill.