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.
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.