Full answer
Research by Dr. Roy Lewicki at Ohio State identified six components of effective apologies; the most important are acknowledging the offense specifically (not just "I'm sorry you feel that way") and offering a plan to not repeat it.
Start by naming exactly what you did wrong — vague apologies feel dismissive. "I'm sorry I missed your graduation because I didn't prioritize it" lands differently than "I'm sorry things happened the way they did."
Take full responsibility without qualifications. Adding "but" or "if" — "I'm sorry if you were offended" — shifts blame to the other person and invalidates the apology entirely. Own your behavior cleanly.
Give the other person time to process. A sincere apology is not a transaction that immediately resets the relationship — the hurt party may need days or weeks before they can accept it, and pressuring a quick forgiveness undermines the repair.