Apologize without blaming.
When a customer senses that you are sincerely sorry, it usually diffuses the situation. Don't blame another person or department. Just say, "I'm sorry about that.”
Ask the customer, "What would be an acceptable solution to you?"
Whether or not the customer knows what a good solution would be, I’ve found it’s best to propose one or more solutions to alleviate his or her pain. Become a partner with the customer in solving the problem.