Girls very rapidly experiencing a quarrel, so before you apologize, wait for some time to the emotions subsided, and she calmed down. A small pause will allow you to relax from the stress the girl to think objectively about what happened. After some time the girl will start to get bored, and then you can try to apologize to her.
It is not necessary to apologize to a girl over the phone or through text messages. The best way to truly apologize is to do it in person or at least to write a paper letter and send it by mail or put them in her mailbox.
Make a girl a compliment, tell her you love her and that she is the only and best girl in your life. Let her know that she stands out from the crowd and that you value and cherish her.
Don't stay on top of what happened a fight. Instead, tell the girl as much good, to call it a return of warm feelings. Comfort the girl and tell him that you sincerely regret what hurt her.
Try also to apologize to her in front of witnesses – if a girl will see that the apology was watched by more than a dozen people, she will not be able to resist and will forgive you. Book for girls a beautiful bouquet of flowers with a card that should deliver the courier at her home address, work or University. The girl must feel that she is dear to you, and that you don't want to lose her.
Make original and unusual things – book for girls performance love serenades, write her poems, ask the lecturer in her University before the beginning of the lecture to announce that you are asking her forgiveness. Make a presentation with pictures, telling your love story.
Try to talk with best friends or the girl's parents – make sure they have taken your side, and also asked the girl to forgive you. Be creative and attentive and in the end, the offended girl will give up and you will receive forgiveness.