Prepare a special gift for someone who is angry at you. When the person receives the gift, the anger will subside.
We find an example of this in the Torah when Jacob told his sons to take the best possible gift to the man in authority in Egypt. (see Genesis 43:11)
Furthermore, sometimes it is beneficial to allow some time to elapse. Even if at the outset of the person's anger nothing you could say would help, after time has passed he will be more open to discussing the matter.
Today, think of someone who has been angry at you. What gift can you give that person that perhaps will make him more open to let go of the anger?