Dear {Recipient},
I know how awful it is when you're counting on someone and he/she lets you down, so that makes it even harder for me to try to find the words to apologize for my late appearance at the {party, business meeting, etc.}.
I am aware that you expected me to be there at {HH:MM}, and that I showed up late, which embarrassed both of us. I never enjoy putting anyone in a situation like that, and I am truly sorry that you had to endure those moments of wondering where I was. And I regret that you had to try to make excuses for my tardiness.
I hope I can make this up to you in the future. Please give me a call as soon as possible so that we can talk, and so that I can apologize in person.
Regretfully,
{Sender}
