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Make sure it is appropriate. Act quickly. Find the appropriate medium for your apology. Move on after apologizing.

Article:
Depending on the setting, an apology may be seen as an admission of guilt, especially if you are apologizing on behalf of your company to customers. If you or your company is not at fault for what happened, you do not need to issue an apology.  Don’t take responsibility for things that are not your fault, and you will avoid over-apologizing, which can weaken your image with co-workers or customers. It is certainly appropriate to express empathy, but you should avoid taking responsibility. You can tell people “I’m disappointed to hear that,” and offer to help resolve the problem, but avoid saying “I’m sorry.” If you are apologizing on behalf of a business to your customers, this may be seen as an admission of responsibility, and you may be held legally and financially liable. Make sure you discuss what happened with a lawyer to discuss any potential legal difficulties before apologizing. This isn’t effective for lots of the smaller mistakes that may happen with customers daily, so you may consider creating company policies for certain mistakes, and how your employees should handle them. If your customers are angry or upset with something your business has done, you need to move quickly. They are more likely to listen to an explanation if you issue it as soon as possible. The longer you delay saying anything, the more angry the future recipient will be. While there are times when you should delay apologizing in order to consult with other people, such as a lawyer, it is important that you get on that as quickly as possible so you can get your message out as soon as you can. Depending on the nature of your error, including what you did and who it was against, there are different mediums you can use to respond.   If your mistake was one that affected all of your clients, an email is a good choice. If your error was posting an offensive or inappropriate message through social media, using that platform as a place to express your contrition. If you need to apologize to someone in your own company, or to a specific client, try to arrange for a face-to-face meeting. If you can’t be in the same place, try video-conferencing, then a phone call. The closer you are able to get to the person you are apologizing to, the better. This will make you look more serious when offering your apology. Once you have apologized, and the apology has been accepted, you both need to be prepared to move past it. Hanging on to the issue will only make the situation more difficult to handle. This goes for recipients too. If someone apologizes to you, and you accept it, there is no need to dwell on the mistake any longer. Bringing it up again will look petty or unprofessional.