Combine the cranberries, sugar, and orange juice in a medium saucepan. Bring to a boil over medium-high heat, stirring occasionally.

Reduce the heat to a simmer and cook, stirring occasionally, until the cranberries pop and the sauce thickens. It should be jammy but still have some visible cranberry pieces. This took about 15 minutes with frozen cranberries, but fresh cranberries should take less than 10 minutes.

Remove the saucepan from the heat. Add a dash of cinnamon and some freshly grated orange zest, then stir in the orange liqueur.

Allow the cranberry sauce to cool, then transfer it to a covered container and refrigerate until chilled. The sauce will continue to thicken as it cools. Serve cold.