Dear Sarah,
I’m so sorry for not meeting you at the airport as we had arranged. I know you were counting on me to help you with your luggage, and I feel absolutely terrible about leaving you to deal with everything on your own.
The reason I completely missed our meeting was that there was an unexpected emergency in my family. My grandmother suddenly became unwell, and I had to stay with my family and help them deal with the situation. Everything happened so quickly that, in the middle of all the confusion, I completely forgot about our arrangement. I realise that this is a terrible excuse, especially as you had just arrived and were probably exhausted after your journey.
I genuinely feel awful about letting you down, particularly because you were relying on me. I hope you weren’t left waiting for too long or had too much trouble getting to your accommodation.
To make it up to you, I’d love to take you out for dinner this weekend. I can also help you with anything you need during your stay, so please don’t hesitate to ask. I really hope you can forgive me, and I promise I’ll make it up to you.