The first tip is NEVER TELL HER TO RELAX The word "relax" is a forbidden phrase in fight. By asking her to relax, man is indirectly indicating that a woman is out of mood and out of control, while she thinks that she is really serious on what she is trying to prove.
The second piece of advice is DON'T EVEN TRY TO EXPRESS LOVE. Telling 'I love you', or 'can I kiss you' type expressions are forbidden in a fight. The immediate answer will be a denial and it will only help to prolong the fight. Woman may consider the expressions as a way to divert her attention and trying to play with her emotions.
I am sure that you must't go on apologizing in any case. Apologizing with a fighting woman many times bring back the negative results. When the man apologizes she just jump into the conclusion that he is mistaken not her. Silence or less-hurting arguments are better to calm down an angry woman.
If you know some other ways how to calm down an angry woman, let me know))