Combine the cranberries, sugar, 1 1/2 cups water, the cherry juice, dried cherries, rosemary and a pinch of salt in a medium saucepan. Bring to a simmer over medium heat and cook, stirring occasionally, until the cranberries burst and the sauce thickens, 15 to 20 minutes. Let cool slightly. Discard the rosemary sprig.
Puree the sauce in a blender until smooth. Strain through a fine-mesh sieve into a serving dish, pressing the sauce through with a rubber spatula. Refrigerate until set, at least 3 hours or overnight.