Combine dates and 1/3 cup port in a small saucepan. Bring to a boil over medium-high heat and cook for 1 minute. Cover and let stand for 10 minutes.
Meanwhile, zest clementine, then peel and separate into segments. Combine the zest, the segments, cranberries, sugar, cinnamon, (if using), and salt in a food processor. Add the dates and their soaking liquid and pulse until coarsely chopped, but not pureed.
Return to pan, add 1/4 cup port, bring to boil and simmer 4-5 minutes until slightly thickened.