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This is assuming that you are the person who is a secretary or a scheduler, and want to apologize to someone who is complaining about how long they have had to wait. The main idea is that you want to ensure someone feels like their opinion has been heard and that you acknowledge that what they said to you is valid.
In addition, it is good to include some steps you might take to prevent something similar from happening again next time.
Dear (Name),
I sincerely apologize for the delay that you endured waiting in Dr. Lu’s office last Monday afternoon. She had several different surgeries scheduled in the morning and was unable to make it to your appointment at the regularly scheduled time. I understand that you had to wait over an hour to get to talk to her about your health situation.
The reason for this delay was a complication in one of the surgeries that she had this morning. Since you insisted on seeing her and not someone else, her schedule had to be rearranged to accommodate what happened. I know she regrets that you had to wait this long and hope you can understand what happened. In the future, we will try to be more cognizant of potential delays and inform you ahead of time that you should expect one, which will hopefully minimize the impact of such delays to you and your plans. Please let us know if there is anything else that we can do for you.
Thank you,
Your name
