Add the black raspberries to a large, heavy-bottomed pot with the water (1/4 cup per quart of fruit). Bring to a simmer over medium heat, mashing the berries as they heat, and cook until they have completely fallen apart and released their juice.
Pour the cooked fruit into a dampened jelly bag or a double layer of dampened cheesecloth set over a bowl and let it drip. Do not squeeze the bag, since that clouds the finished jelly. Measure the strained juice.
Combine the strained juice and sugar in a clean, deep, heavy-bottomed pot. Bring to a boil over high heat, stirring until the sugar has dissolved.
Boil hard, stirring often so it does not scorch, until the jelly reaches the gel point (220°F on an instant-read thermometer, or until a spoonful sets up and wrinkles on a plate chilled in the freezer). This usually takes about 8 to 10 minutes but can take longer.
Remove from heat and skim off any foam. Ladle the hot jelly into prepared jars, leaving 1/4 inch headspace. Wipe the rims, center the lids, and screw the bands to fingertip tight.
Process in a boiling water bath canner for 10 minutes, adjusting for altitude. Turn off the heat, let the jars rest 5 minutes, then remove and cool undisturbed for 12 to 24 hours before checking seals.