Rinse the cranberries: Rinse the fresh cranberries under cold water and pick through them, discarding any that are soft, shriveled, or discolored.
Combine the liquid base: In a medium saucepan, combine the sugar, orange juice, water, orange zest, cinnamon stick, and salt. Stir well so the sugar begins to dissolve.
Bring to a boil: Set the saucepan over medium-high heat and bring the mixture to a full boil, stirring occasionally so nothing sticks to the bottom.
Add the cranberries: Stir in the fresh cranberries and reduce the heat to medium-low so the mixture settles into a steady simmer rather than a hard boil.
Simmer until berries pop: Cook for about 10 minutes, stirring occasionally, until you hear the berries popping and most of them have burst open.
Check the texture: The sauce is ready when it coats the back of a spoon in a thin glossy layer; it will continue to thicken as it cools.
Remove the cinnamon stick: Take the pot off the heat and fish out the cinnamon stick, discarding it so it doesn't overpower the sauce as it sits.
Cool at room temperature: Let the sauce cool in the saucepan or a heatproof bowl for about 30 minutes before covering it.
Transfer to a container: Spoon the cooled sauce into an airtight container, pressing a piece of plastic wrap directly onto the surface if you want to prevent a skin from forming.
Chill before serving: Refrigerate the sauce for at least 4 hours, though overnight gives the best texture and allows the flavors to deepen.
Serve cold or at room temperature: Bring the sauce out of the fridge about 20 minutes before your meal if you prefer it closer to room temperature, or spoon it straight from the fridge for a firmer texture.