Toast the coriander seeds in a dry medium saucepan over medium heat, shaking often, 3 to 4 minutes. Transfer to a paper towel, fold to cover, then crush the seeds with a rolling pin. Return to the saucepan.
Add 1 1/2 cups water, the sugar, cranberries, kumquats and 1/4 teaspoon salt to the pan. Bring to a boil, then reduce to a simmer and cook until the berries burst and the sauce thickens, 18 to 25 minutes. (If the berries are not bursting after 15 minutes, gently mash with a spoon.) Let cool.
Transfer the sauce to a bowl and refrigerate until chilled and thickened, at least 3 hours.
Make the sauce up to 1 week ahead; cover and refrigerate.