Some marriages were meant to be. Some were meant to be friendships. Once the divorce is over, depending on how messy it was, you'll know if the two of you are in good enough emotional states to remain friends. Chances are, if you were close enough to be married, there are still a lot of shared interests there to make a great friendship. Sometimes the chemistry that didn't work within the intensity of a marriage can work wonderfully in the more relaxed realm of a friendship. If you and your ex find you still like each other, give this different type of connection a try.
Meet for lunch. Find out if your ex is interested in being friends.
Try doing something on neutral territory, like going out for a movie or pizza. Include friends that both of you love.
The marriage is over, so it's not fair bringing up any negative leftovers from that union. Treat this friendship as the new installment. Let go of the past and enjoy this present.
Use your great knowledge of your ex's heart to really celebrate who he is, and your connection. Encourage a close relationship by calling often, respecting any new boundaries and being there for him as any good friend would.