if it's a face to face quarrel, i would see her reactions after
the quarrel, if she is pissed off, don't want to listen, well i
just hug her closely, and kiss her and than look at her in the eyes
& say "I Sorry, I didn't mean to upset you" (make sure you mean
it!)
Add a joke after that, that will make a smile, if i were you, I'll
say "don't frown, or be angry, you will get more wrinkles if you do
that..than will not be pretty le wor..
Something like that. (edit accordingly to your preference)
than take her somewhere to eat her favourite food/snacks, girls
usually like ice-creams. than see her back home, end of with a good
bye kiss followed by saying you love her.