I took a course called Tuning in to kids, which talked a lot about "emotional coaching". Although the course was geared towards relationships between parents and children, many of the tips can be applied to adult relationships as well. The first step is to maintain control of your own emotions. If you are feeling very passionate and intense, then chances are the argument that can be resolved with an amicable solution, will result in a flared up battle that will end up in resentful things being said that can never be taken back. Escalating a conflict will never lead to resolution, in fact, it will lead to more conflicts. So first step is to remain calm. You can do that by drinking a glass of water, by excusing yourself for 10-15 minutes, and lock yourself in a room or go for a walk. Once you are calm, you can rationalize your thoughts. Then try to understand why the person is willing to have a fight over the issue at hand. If you can put yourself in their shoes, you will be able to find the reason of the conflict and handle it better. If you are unable to understand, it is not a bad idea to actually talk and ask questions which lead to the bottom of the reason.
There is a great book called "I only say this because I love you" by Deborah Tannen, which is a must read for all adults.
Being respectful, listening to each other rather than yelling, trying to understand the underlying issues, being open about problems, having an open discussion by laying out all the cards on the table, not involving third parties are great ways to resolve any conflicts or at least deal with many conflicts in a relationship.