What does it take to make a heartfelt apology?

As with all communication listening is key. Saying “I’m sorry” is rarely the first part of a good apology. Before saying anything, the other person has to understand your hurt. Usually, that means listening. So, ask them to back up and let you tell them about your experience of hurt, about how their behaviour has affected you.
The second step, to make a sincere statement of responsibility and empathy, is much easier if Step One has taken place—and much more convincing. If your apologizer has gotten this far with you, you can probably sense good-willed effort; nonetheless, your relationship will benefit from your holding high standards for this step.
The third step requires the person to make restitution, that is, to make up for the wrong or hurt. Making it right requires a person to put their words or intentions into action. Reluctance to try again or to extend in this way is another sign that your apologizer isn’t really interested in making a thorough apology.
But Step Four, making sure it doesn’t happen again, is the pudding in which the proof lies. It will take time for you to see if a true change has taken place, but a convincing plan helps you stay motivated to see it through.
Making your way through this process is energy-intensive for you both and its outcome only fully reveals itself over time. But if your apologizer follows these four steps, they will convince you of their sincerity.