Preparation Peel, quarter, and core quinces, reserving peel and cores, then cut quarters into 1/4-inch pieces. Tie up peel and cores in cheesecloth. Bring water and sugar to a boil in a 4-quart heavy saucepan, stirring until sugar is dissolved, then add quince and cheesecloth bundle and simmer, partially covered, until quince is tender, about 1 1/2 hours. Add cranberries and simmer, uncovered, stirring occasionally, until cranberries burst and soften, 8 to 10 minutes. Drain mixture in a large medium-mesh sieve set over a bowl, discarding cheesecloth bundle and reserving cranberry solids, then return cooking liquid to pan and boil, uncovered, until syrupy and reduced to about 1 1/2 cups, 5 to 10 minutes. Stir together syrup and cranberry mixture in bowl, then cool to room temperature. Cooks' note:Cranberry quince sauce can be made 3 days ahead and chilled in an airtight container.
Preparation Peel, quarter, and core quinces, reserving peel and cores, then cut quarters into 1/4-inch pieces. Tie up peel and cores in cheesecloth. Bring water and sugar to a boil in a 4-quart heavy saucepan, stirring until sugar is dissolved, then add quince and cheesecloth bundle and simmer, partially covered, until quince is tender, about 1 1/2 hours. Add cranberries and simmer, uncovered, stirring occasionally, until cranberries burst and soften, 8 to 10 minutes. Drain mixture in a large medium-mesh sieve set over a bowl, discarding cheesecloth bundle and reserving cranberry solids, then return cooking liquid to pan and boil, uncovered, until syrupy and reduced to about 1 1/2 cups, 5 to 10 minutes. Stir together syrup and cranberry mixture in bowl, then cool to room temperature. Cooks' note:Cranberry quince sauce can be made 3 days ahead and chilled in an airtight container.