I think it depends on what it is. If you don't mind sharing what you want to apologize for, maybe I could help better... but let's say you cheated on her. For one thing, I would need him to be completely honest and tell me why he did it. Maybe it was something that I was doing without knowing it that drove him to cheat, for example. If it was something like yelling at me, having an outburst... I would need to see time go by without it happening again. I always feel opening up and explaining yourself are better than gifts. I want the heart-to-heart, you know? Everyone makes mistakes and it's just determining why and how to mend the situation
When he acknowledges not only that what he said was hurtful, but WHY it was hurtful.
If I had a really big butt and he teased me, a real apology would be something like:
"I crossed the line when I said that. I'm sorry, I forgot how sensitive you are about it. I was only kidding, I never meant to hurt your feelings. It won't happen again."
He acknowledges he went too far, gives acknowledgment that he understands why I was hurt and gives validity to my feelings, whether he agrees with them or not. Then he makes a promise never to go there again.
I don't need flowers or anything as long as he is genuinely sorry. A lighthearted "sorry" won't cut it if feelings were hurt.
It has nothing to do with what you give her, it's about realizing/acknowledging what you did wrong, why it was wrong and being actually sorry for it. That's what makes it sincere.
There's a big difference between a quick "I'm sorry" uttered over and over and eventually screamed at each other and a guy who calmly looks you in the eye and says "I'm sorry I did X, I know it made you feel Y and I'll never/try to never do it again"