Place a couple of spoons in the freezer to chill while making the jam. Thoroughly wash the fresh grapes. If they are frozen, allow them to defrost at room temperature. Remove the skins from each grape: for frozen grapes, simply pinch one end of grape and squeeze out the pulp. For fresh grapes, cut a small X into one end of the grape with a paring knife, then squeeze out the pulp. Separate the pulp and skins.

Place the grape pulp into a small saucepan over medium heat. Simmer for about 5 minutes, stirring occasionally. Pulse the cooked pulp in a food processor a few times, then strain through a medium-mesh sieve to remove the seeds. Or, put the pulp through a food mill to remove the seeds. Discard the seeds, and put the strained pulp back in the saucepan.

Put the skins in the food processor and pulse several times until they are finely chopped. Add the chopped skins to the saucepan.

Bring the strained pulp and chopped skins to a simmer over medium heat, then cook for about 10 minutes until the skins have softened. If you want a smooth-textured jam, blend with an immersion blender (or regular blender) to reach the desired consistency.

Add in the rest of the sugar, bring to a boil, and boil for one minute.

Remove one of the spoons from the freezer and scoop out a little hot jam. Allow it to cool on the spoon for a moment, and check that the jam is jelling. If the jam on the spoon looks thick and viscous, and has little wrinkles of surface tension around the edges, then it is set. If it is still runny, add another tablespoon of pectin to the jam and boil for 1 minute. Test for jell with the other frozen spoon. Taste the jam for sweetness. (If the jam needs to be sweeter, add additional sugar to the jam mixture. Boil the additional sugar in the jam for 1 minute to ensure that it has dissolved.)

Scoop the jam into jars, and store in the refrigerator for up to 2 weeks. Or, freeze the jam for up to 3 months.

To can the muscadine jam, ladle the hot jam into hot, sterilized jars (you can use clean, hot jars that have not been sterilized, but the processing time will be longer). Wipe the rims of the jars with a damp cloth or paper towel to remove any sticky jam residue. Immediately place a warmed lid on the jar, then twist a lid ring so that it is secure, but not too tight.

Process the jars in boiling water that sits at least an inch above the tops of the jars. Process sterilized jars at a full, rolling boil for 5 minutes (process for 10 minutes if the jars were hot and clean, not fully sterilized). If you live at an elevation of over 1000 feet, add 1 minute of processing time for each 1000 feet of altitude.

After the processing time, turn off the heat and allow the jars to sit in the water for 5 minutes so the contents can settle and the boiling can subside. Remove the jars carefully with a jar lifter and place them onto a towel or cooling rack (avoid putting them directly on a cool surface). Allow them to cool at room temperature for 12-24 hours. Put any unsealed jars into the refrigerator to be eaten first. Store unopened, sealed jam in a cool, dark place for 6 months to a year.