Crush black raspberries in a bowl. Pour berries into a sieve or cheesecloth over another bowl; let hang and drip into the bowl until dripping stops. Press gently. Measure 3 cups juice and pour into a large pot.

Stir lemon juice into the juice in the pot. Stir in sugar. Bring mixture to a full, rolling boil over high heat, stirring constantly. Stir in pectin quickly. Return to a full boil and boil exactly 1 minute, stirring constantly. Remove from heat. Skim off any foam from mixture using a metal spoon.

Inspect canning jars for cracks and rings for rust, discarding any defective ones. Immerse in simmering water. Wash new, unused lids and rings in warm soapy water.

Ladle jelly mixture quickly into hot, sterilized jars, filling within 1/8-inch from tops. Run a clean knife or thin spatula around the insides of the jars to remove any air bubbles. Wipe rims with a moist paper towel to remove any residue. Top with lids and screw rings on tightly.

Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower jars 2 inches apart into the boiling water using a holder. Pour in more boiling water to cover jars by at least 1 inch. Bring to a rolling boil, cover, and process for 5 minutes.

Remove the jars from the stockpot and let rest, several inches apart, for 24 hours. Press the center of each lid with a finger to ensure the lid does not move up or down. Remove the rings for storage and store in a cool, dark area up to 1 year. Refrigerate opened jellies for up to 3 weeks.