Combine sugar, ruby port or red wine, orange juice, cinnamon stick, and salt in a saucepan, then bring to a boil over medium-high heat. Stir until the sugar dissolves, and keep the sauce actively bubbling for about 1 minute as it reaches a full boil (visual cue: rolling bubbles across the surface).

Add fresh cranberries, reduce to a simmer, and cook for 10-12 minutes, stirring occasionally. Continue until the berries burst and the sauce thickens (visual cue: thicker, syrupy coating on the spoon).

Remove from heat and stir in Grand Marnier or orange liqueur and orange zest. Keep stirring until fully incorporated and glossy (visual cue: even ruby color with no streaks).

Discard the cinnamon stick. Check the sauce for any remaining cinnamon pieces before cooling (visual cue: no visible stick segments).

Cool the sauce to room temperature, then chill before serving. Serve cold for best thickness (visual cue: sauce firms slightly and holds shape on a spoon).