Wash the cherries thoroughly under cool running water and remove the stems. You do not need to pit them, since you will be extracting juice, not making jam.
Add the cherries and 4 cups of water to a large, heavy-bottomed pot. Bring to a boil over medium-high heat, then reduce to a simmer. Cook for about 20–25 minutes, gently crushing the cherries with a potato masher as they soften, until very soft and the juice is richly colored.
Set a large bowl under a fine-mesh strainer lined with a double layer of cheesecloth (or a jelly bag). Carefully pour in the hot cherry mixture. Let it drain for at least 1–2 hours, or overnight in the refrigerator for a clearer jelly. Do not squeeze the cloth too hard; a gentle squeeze at the end is fine.
Measure out 4 cups (960 ml) of strained cherry juice. If you are short, top off with a little water or unsweetened cherry juice. If you have extra, reserve or freeze it for another use.
While the juice drains, wash jars, lids, and bands in hot, soapy water and rinse well. Keep the jars hot in a 200°F (95°C) oven or in simmering water so they do not crack when filled with hot jelly. Prepare a canning pot or deep stockpot with a rack and simmering water.
Pour the 4 cups of cherry juice into a large pot. Stir in the bottled lemon juice and powdered fruit pectin, whisking well to avoid lumps.
Place the pot over high heat and bring the mixture to a full rolling boil, stirring constantly. A full rolling boil does not stop bubbling when stirred.
Add all of the sugar at once, stirring constantly until dissolved. Return to a full rolling boil and cook for 1–2 minutes, stirring. Skim off any foam that forms; you can add a small pat of butter to help reduce foam. The jelly will look glossy and slightly thickened.
To test the set, place a small spoonful of hot jelly on a chilled plate. Let it sit for a minute, then push it gently with your finger. If it wrinkles slightly, it is ready. If still liquid, boil another minute and test again. The gelling temperature is around 220°F (104°C) at sea level.
Working quickly, ladle the hot cherry jelly into hot jars, leaving 1/4 inch (0.5 cm) headspace. Wipe the rims with a clean, damp cloth. Place lids on top and screw bands on just fingertip-tight.
Place the filled jars on the rack in the canning pot, ensuring they are covered by at least 1–2 inches of water. Bring to a full boil, then process for 10 minutes, adjusting time for altitude if necessary.
Turn off the heat and let the jars rest in the water for 5 minutes. Carefully remove them and place on a towel-lined counter. Do not tilt or shake the jars. Let sit 12–24 hours, then check seals; lids should be concave and not flex when pressed.
Label each jar with the date and “Cherry Jelly.” Store sealed jars in a cool, dark place. Refrigerate any jars that did not seal and use those first.