In a blender or food processor, puree the plums. If they are firm, chop them up first.
Push the plum puree through a food mill or fine mesh strainer and discard the skins. Add the puree to a dutch oven or heavy bottom saucepan.
Use a vegetable peeler to peel 4 large strips of zest from the orange or clementines. Juice the fruit and add 3 tablespoons of juice to the pot along with the zest. Stir in the vanilla, cinnamon, allspice and honey.
Bring the mixture to a boil, stirring periodically, and then turn the heat down to a simmer. Cook for 75-80 minutes, uncovered, and use tongs to remove the zest after 20 minutes. Stir frequently, scraping a heat proof spatula against the bottom of the pan to make sure nothing sticks.
Allow to cool and then store in the refrigerator.
Notes
Less ripe plums are often more tart while ripe plums are more sweet. For a nice flavor balance, use a mixture of both ripe and semi-ripe plums. If you use all ripe plums you might want to use less honey (and possibly a tablespoon or two of fresh squeezed lemon juice for tartness). If your plums are very tart to begin with, add more honey to taste.