Apologising
If you're replying to a tricky letter or a complaint, or are dealing with a difficult problem, put yourself in the reader's shoes. Be professional, not emotional.
You may have to give a firm, unwelcome answer, but be as helpful and polite as possible. If you are going to apologise, do so early. If the problem is your fault, say so.
Apologise completely and concisely, sympathetically and sincerely. And whether it is your fault or not, try to emphasise what you can do for the other person.