Simmer grapes and water, mashing occasionally, until very soft: Combine fruit and water in a saucepan. Bring to a boil, reduce to a simmer, and cook, partially covered, mashing occasionally with a potato masher, until fruit is very soft, 10 to 15 minutes.
Drain mixture using fine-mesh sieve: Transfer mixture to a fine sieve set over a heatproof bowl; let drain without pressing on fruit, 4 hours.
Strain again using cheesecloth; measure juice: Strain again through sieve lined with damp cheesecloth. Measure juice; you will have 3 to 4 cups.
Boil juice; add sugar and remaining ingredients: In a large heavy-bottomed pot, bring juice to a boil. Add ¾ cup sugar for each cup of juice. Add lemon juice and ¼ teaspoon salt. Return to a boil and cook, stirring frequently, 8 to 12 minutes.
Check for doneness using spoon test; skim foam: To test if jelly is done, dip a large metal spoon in, lift it horizontally above pot, and let mixture drip back in. Jelly is done when mixture has thickened slightly and drops of it slide together off spoon in a sheet. (Temperature should register 221 degrees on a candy thermometer.) Skim foam from top.
Ladle into jars; let cool, then cover and label: Ladle jelly into clean containers, leaving ¾ inch of headroom. Let cool completely. Cover, label, and refrigerate up to 1 month, or freeze up to 1 year.
