Well.... it depends on whether your saying sorry to a boy or a girl, and if your a guy or a girl
If you are saying sorry to a GIRL and you are a GUY.... I would suggest just explaining why your sorry, and maybe if you would like giving said girl a hug, that's what I would want.
If you are saying sorry to a GIRL and you are a GIRL.... Again, explain why your sorry, and if that doesn't work, just let her simmer down... Hope for the best.
If you are a GUY saying sorry to a GUY.... I would suggest saying sorry, and hoping they don't hold a grudge... people do that sometimes.
Hope this helps!
-D :D