Put the wine, sugar, salt and 1/2 cup water in a high-sided medium skillet and bring to a boil over medium-high heat. Add the quince and bring to a boil. Reduce to a simmer and cook, partially covered, until the quince slices are very tender and translucent but still hold their shape, 20 to 30 minutes.
Remove the quince to a bowl with a slotted spoon, leaving the syrup in the skillet. Return the heat to high and simmer the syrup until thickened, about 3 minutes. (You should have 1/3 cup syrup when finished.) Pour the hot syrup over the quince and stir in the crystallized ginger. Serve warm, at room temperature, or cool. The quince will keep covered in the refrigerator for 3 days.
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