1. Place a saucer with 5 metal teaspoons in your freezer for testing the jam later.
2. Working over a small, nonreactive saucepan, gently squeeze the flesh from each grape. Put the skins in a bowl and set aside. Bring the grape pulp and juices to a simmer over medium heat, cover and cook until soft, about 4 minutes. Push the pulp through a fine-mesh strainer and discard the seeds.
3. In a wide, nonreactive pot, combine the grape pulp with the sugar, lemon juice, orange zest, orange juice and grape skins. Bring to a boil over high heat. Continue to cook, stirring frequently, until glossy and thickened slightly, about 20 to 30 minutes. (If the jam starts sticking, lower the heat.) After 20 minutes, test the jam for doneness (see Note) to avoid overcooking the fruit.
4. When the jam is done, skim off any foam from the surface with a spoon. Transfer the jam into sterilized 8-ounce jars and process according to the manufacturer's instructions. The jam will keep for 1 year.
Note: To test the jam for doneness, remove it from the heat and transfer a half-spoonful to one of the frozen spoons. Place the spoon in the freezer for 4 minutes, then remove and feel the underside of the spoon. It should be neither warm nor cold; if it's still warm, return it to the freezer for another minute. Tilt the spoon vertically to see how quickly the jam runs; if it is reluctant to run and has thickened to a spreadable consistency, it is done. If it runs quickly, cook it for another minute or two, stirring, and test again as needed.