When you have your own business it's understandable that you will encounter clients that are not too happy with your service or even irate clients who make extreme demands, often times demands you cannot accommodate. It's important to keep your cool when these situations arise. Though you may lose your client, regardless of how you react to an outburst, you should make it a point to stay professional in all difficult situations.
If your get an nasty email from a client, take some time to cool off yourself, it's only a human reaction to feel defensive when someone is criticising all you work for, so be sure to take some time to cool off. When you're calm, take the key points out of the email and see where you made the mistake, it's important to not over explain your mistakes, chances are that the mistake is something you could have prevented, but over explaining will not make things better, only worse. Once you figure out what you did wrong, be sure to call the client, as emails can sometimes be misread in an angry or sarcastic tone. If the client is not available by phone be very careful that you word your email back in a professional manner, and minimize any room for misinterpretation. Here's an example of an email exchange that has been turned positive.
Client: I'm extremely upset, I ordered flowers and candy for my wife to be delivered to her office, I specifically told the representative at your company that she has a mild peanut allergy and that I needed the candy to be plain M&Ms instead of peanut, I also requested that there be 11 red roses and one pink rose, I called twice to confirm this, the card even referenced the pink rose. Instead my wife not only received peanut candy, but 11 pink roses and one red rose. I have never been more disappointed in a company before, I should have asked for peanut candy and 11 pink roses, then you would have got it right! Be sure to take my name on your mailing list, because I'll never be doing business with you again! Thanks for the worst service ever!
Company: First of all I would like to personally apologize for the service you have encountered, we are here to provide good service to you and frankly we failed. Although a little late, we've already set up an appointment to deliver a special package to your wife on Monday, should this be a problem please let me know. I would also like to take the time to thank you for your feedback and let you know that I've attached a gift coupon to this email good towards a future purchase with our company. Again I do apologize for the inconvenience, and I hope you find the kindness to let us correct this mistake.
The email is simple and to the point and also offers a way to fix the problem. The main point is to stay calm when your client is angry, usually things will work out, if you're heated the situation will only escalate.