Place cherries, apple juice, lemon juice, and pectin into a large saucepan over medium heat; bring to a boil, and mix in the sugar. Cook the jam at a rolling boil for 2 minutes, stirring constantly. Remove from heat and skim off any foam.

Sterilize the jars and lids in boiling water for at least 5 minutes. Pack the cherry jam into the hot, sterilized jars, filling the jars to within 1/4 inch of the top. Run a knife or a thin spatula around the insides of the jars after they have been filled to remove any air bubbles. Wipe the rims of the jars with a moist paper towel to remove any food residue. Top with lids, and screw on rings.

Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil over high heat, then carefully lower the jars into the pot using a holder. Leave a 2 inch space between the jars. Pour in more boiling water if necessary until the water level is at least 1 inch above the tops of the jars. Bring the water to a full boil, cover the pot, and process for 15 minutes, or the time as recommended by your county Extension agent.

Remove the jars from the stockpot and place onto a cloth-covered or wood surface, several inches apart, until cool. Once cool, press the top of each lid with a finger, ensuring that the seal is tight (lid does not move up or down at all). Store in a cool, dark area.