Rinse the cranberries and pick out any soft or shriveled berries.
Combine the sugar, water, orange juice, orange zest, and salt in a medium saucepan. Bring to a boil over medium-high heat, stirring until the sugar dissolves, 2–3 minutes.
Add the cranberries and return to a gentle boil. Reduce heat to maintain a lively simmer and cook, stirring occasionally, until most berries have burst and the liquid thickens slightly, 10–12 minutes. Doneness cue: the sauce should lightly coat the back of a spoon.
Remove from heat and let cool to room temperature until thickened and set, 30–45 minutes. For a smoother texture, mash the berries lightly with a spoon while cooling.
Transfer to a bowl, cover, and serve at room temperature or chilled. For best flavor, refrigerate at least 1 hour and up to 1 week.