Wash jars, lids, and bands. Place jars on a rack in a deep pot or canner, cover with water, and bring to a bare simmer to keep hot. Keep lids and bands at room temperature, following manufacturer guidelines.
Rinse the sour cherries, remove stems, and pit them, catching any juices.
In a wide, nonreactive pot, combine the pitted sour cherries and granulated sugar. Toss gently to coat. Cover and macerate in the refrigerator 6–12 hours (8 hours is typical) until a deep syrup forms and most sugar dissolves.
Set the pot over medium heat and stir until any remaining sugar dissolves. Increase to medium-high and bring to a steady boil, stirring gently to avoid breaking the fruit. Skim and discard foam as it rises.
Cook at a brisk simmer/low boil, 20–30 minutes, until the syrup reaches 220°F on a thermometer, or until it passes the sheet test (syrup drips from a spoon in wide, slow sheets). The cherries should remain plump and suspended in a glossy, clear syrup.
Stir in the bottled lemon juice and boil 2 minutes. Skim again if needed, then remove from heat and let the preserves rest 5 minutes so fruit settles evenly.
Working with one hot jar at a time, ladle hot cherries and syrup into jars, leaving 1/4 inch headspace. Remove air bubbles, adjust headspace, wipe rims clean, and apply lids and bands fingertip-tight.
Process jars in a boiling-water bath for 10 minutes, starting timing once the water returns to a full boil. At 1,001–6,000 ft elevation, process 15 minutes; above 6,000 ft, process 20 minutes.
Transfer jars to a towel-lined surface and cool undisturbed 12–24 hours. Check seals, wipe jars, label, and store in a cool, dark place for up to 1 year. Refrigerate after opening and use within 1 month.