Combine the sugar, orange juice, water and cinnamon stick in a medium saucepan. Bring to a boil over medium heat, stirring until the sugar dissolves.
Add the cranberries and return to a boil. Reduce the heat to a lively simmer.
Cook, stirring occasionally, for 8–10 minutes. The berries will pop and the sauce will begin to thicken.
Stir in the zest and salt. Press some of the berries against the side of the pan if you like a smoother sauce.
Remove the cinnamon stick. Taste and add a little more sugar if needed while the sauce is hot.
Let cool to room temperature; it will thicken considerably. Serve at room temperature or chilled.
