Discard any cranberries that are dried out or discolored and rinse.
Place cranberries in a saucepan with the sugar, orange zest, orange juice, spiced rum, and a cinnamon stick.
Cover the pan and cook over medium heat for about 15 minutes, stirring every couple of minutes. The cranberries will begin to pop.
When most of the cranberries have popped, remove the pan from heat. If the sauce looks too watery, the pectin in the cranberries will make the sauce thicken as it cools. For a thinner texture, add a little more water or orange juice.
Serve the sauce cold or at room temperature.
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