Prepare a boiling-water canner with a rack; wash 5 half-pint jars and keep them hot in the canner. Prepare lids and rings according to manufacturer’s directions.
Combine the rinsed redcurrants and water in a wide preserving pan. Bring to a simmer over medium heat, then cook, stirring and gently crushing the fruit, until the currants collapse and release their juice, 10–15 minutes.
Line a sieve with a damp jelly bag or several layers of damp cheesecloth and set over a deep bowl. Pour in the hot fruit pulp and let it drip without pressing until the dripping stops, 4–12 hours (overnight is ideal) for a clear jelly.
Measure the collected juice—you should have about 4 cups. Rinse and dry the preserving pan; return the juice to the pan and add 4 cups granulated sugar (use 1 cup sugar per 1 cup juice; adjust the sugar if you have more or less juice). Warm over medium heat, stirring, until the sugar is fully dissolved, 3–5 minutes.
Increase heat to high and bring to a full rolling boil. Boil hard, stirring occasionally, until the jelly reaches setting point, 8–12 minutes. Doneness cues: it should reach 220°F/104–105°C at sea level, sheet from a spoon, and wrinkle on a cold plate. Skim foam as needed.
Working quickly, ladle the hot jelly into hot jars, leaving 1/4 inch headspace. Wipe rims, apply lids, and screw bands on fingertip-tight.
Process the jars in a boiling-water canner for 10 minutes (start timing when the water returns to a full boil). At higher altitudes, add 5 minutes for 1,001–6,000 ft and 10 minutes above 6,000 ft.
Remove jars to a towel-lined rack and cool undisturbed 12–24 hours. Check seals, wipe jars, and label. Store sealed jars in a cool, dark place; refrigerate any unsealed jars and use first.