Dear {Recipient},

I apologize for flaking out on our lunch date {yesterday/the other day}. I was really looking forward to spending some time with you and chatting about {topic}, so I was just as upset as you were when I had to cancel unexpectedly due to {reason}. I hope you understand.

Of course, I'd still love to have lunch with you, so please let me know your availability this week or next. I'm looking forward to hanging out with you really soon!

Warm regards,

{Your Name}

Dear {Recipient},

Please accept my apologies for not showing up at {event} {yesterday/last weekend/etc.} despite RSVPing “yes.” I was really looking forward to the event; sadly, I wasn't able to attend at the last minute due to {reason for absence}.

I'm really sorry I couldn't be there to celebrate {occasion} with you. I didn't {call/text} you anymore because I didn't want to bother you on your big day. Anyway, I wish you {a happy birthday/all the best/etc.} and I hope we can catch up soon!

Warmly,
{Your Name}

Dear {Recipient},

I'm writing to offer my apologies for giving a bad first impression during our meeting on {date}. I wasn't feeling like myself that day, so I'm sorry if I made you uncomfortable.
If you would give me a chance to redeem myself, I'd like to invite you to {event} on {date}.

Many of our mutual friends are also attending, so you don't have to worry about any potential awkward moments. I hope to see you there!

Kind regards,

{Your Name}