Prepare a 1-quart canning jar, new lid, and ring according to the manufacturer's directions for sterilized jars. Keep the jar and lid hot until you fill them. Place the grapes in the hot jar and add the sugar.
Pour boiling water into the jar until it's about half to two-thirds full, then stir well until the sugar dissolves completely.
Add enough additional boiling water to fill the jar, leaving ¼ inch of headspace at the top. Wipe any drips from the rim and sides with a clean damp cloth.
Cover with a hot lid and tighten the ring firmly. Repeat with as many jars and grapes as you like. Set the jars on a rack in a canner or deep pot of boiling water, covered by at least 1 to 2 inches of water, and boil for 10 minutes.
Remove the jars with canning tongs and set them on a towel or rack to cool overnight.
When completely cool, check the seals. Each lid should be down in the center and stay down when pressed. Store sealed jars in a cool, dark, dry place for at least 3 months and up to 1 year.
When you're ready to use the juice, strain the liquid through a fine mesh sieve, discard the solids, and refrigerate the juice in a clean jar for up to 1 week.