Gather up your courage. In her book, "Dignity: The Essential Role It Plays in Resolving Conflict," Donna Hicks notes that "the temptation to save face is as powerful as our fight or flight instinct." She believes that that people are highly motivated to do whatever they have to in order to protect themselves. The result is that making an apology can be a fear-inducing experience. Reassure yourself that these feelings are normal and can be overcome with the intention to do right.

Tell the person you offended or hurt that you understand how he feels. Empathy lends sincerity to your apology, and saying that you also would feel hurt if you were on the receiving end can go a long way toward making him feel better -- and won't compromise your dignity.

Keep your apology simple and to the point. Don't blather on about how you were such a jerk to have cancelled a night out. Just say you are sorry that you didn't plan better and that you know you hurt the person's feelings. Continuing to say you're sorry after you have already done so will only lend an air of desperation to your point.

Resist the impulse to maintain your dignity by shifting the blame to the other person. Telling her that you're sorry she took your comment the wrong way won't preserve your dignity -- it'll make you appear insensitive and insincere. Bite the bullet and accept responsibility for the action for which you are apologizing, even if you think it was not entirely your fault.

Offer to make reparations if necessary. A study published in the May 2010 journal "Organizational Behavior and Human Decision Processes" found that the effectiveness of an apology depends on the point of view of the person being apologized to. People who are relationship oriented may forgive you when you express empathy, but individuals who tend to be autonomous and concerned with personal rights are more likely to forgive when restitution is offered. If you're apologizing for smashing the television remote when your favorite team missed what might have been a winning touchdown, offer to replace the remote. You'll appear responsible, not desperate.

Avoid asking the person to forgive you. Not only does this come across as needy and somewhat desperate, but it requires the other person to make an effort on your behalf. When you apologize, you shouldn't expect anything from the other person other than an acknowledgement that she heard what you said. Forgiveness will likely come later, after the person has had the opportunity to process what you've said.