Wash the fruit and remove the stems. Place the fruit in a large bowl, and using your hands, a fork, or a potato masher, squeeze the grapes. Place the fruit in a large, stainless steel or enamel pot, and using your hands, mash until no large pieces of fruit remain. Add just enough water to keep the mixture from sticking and bring to a boil over high heat. Decrease the heat to low, and simmer until very juicy, about 20 minutes. Transfer the mixture to a jelly bag and allow to hang over a bowl for at least 6 hours or overnight. (I usually hang it on a cabinet doorknob over the kitchen counter and place a pot or large measuring cup underneath.) Measure the juice; you should have about 8 cups.
When you are ready to make the jelly, place a wire rack on a rimmed baking sheet. (This will help with cleanup for any possible spills.) Place several small plates in the freezer to use later to test the consistency of the jelly.
Sterilize eight 1/2-pint canning jars and lids in boiling water. Remove the jars from the water and place upside down to drain on the prepared rack. Place lids in a small saucepan over very low heat to simmer while you prepare the jelly. Do not boil the lids.
In a large, heavy-bottomed saucepan, combine the scuppernong juice (you should have about 16 cups, or 4 quarts), sugar, lemon juice, and salt. Bring the mixture to a boil over high heat, stirring occasionally. The mixture will bubble up, rising high up the sides of the saucepan. Using a slotted spoon, skim off any light-colored foam as it collects on the edges. Cook the jam until it reaches the jelling point, 220°F on an instant-read thermometer, about 30 minutes. (Dribble a few drops on the frozen plate; if the jelly is about to set, it will crinkle on the plate when you push it with your finger.)
Remove the jam from the heat. For each jar, insert a canning funnel and carefully ladle in the jelly, allowing at least 1/4 inch of headroom. Clean the rims of the jars with a clean, damp towel, and tightly secure the lids.
Using tongs, place the jars on the rack in the canner. The water should cover the jars by at least 1 inch. Cover the canner. Return the water to a boil and boil gently for 5 minutes. Using tongs, transfer the jars to a towel to cool. If the seal works and fits properly, the metal lid will be slightly concave within 24 hours of processing.
Store the unopened jars of jam at room temperature for up to 1 year. Once the jam is opened, store in the refrigerator for up to 1 month.
Variation: For refrigerator or freezer jam, transfer the mixture to sterilized freezer-safe plastic containers or freezer-safe jars with lids, leaving 1 inch of headroom. Freeze for up to 1 year or refrigerate for up to 1 month.