Pick through the cranberries and discard any that look shriveled or mushy. Rinse the remaining cranberries well, then place them in a medium saucepan with the sugar, orange zest, orange juice, and cinnamon stick. Give it a stir, then place the pan over medium heat. Cover the pan with a lid and cook for 15 minutes, stirring the mixture every 5 minutes to ensure the bottom doesn't burn.

After 15 minutes, the cranberries should all be popped. Remove the pan from the heat, and remove the lid. The sauce will look very liquid, but as it cools, the sauce will thicken up significantly. After the sauce has cooled completely, you may add additional water if you desire a thinner texture. Remove the cinnamon stick and serve the cranberry sauce at room temperature or chilled.