Place the tomatoes in a saucepan with a lid and simmer over medium heat, stirring frequently, for 10 minutes. Stir the lemon zest, allspice, cinnamon, cloves, lemon juice, and pectin into the tomatoes. Place the saucepan over high heat. Stirring constantly, bring the tomato mixture to a boil; immediately upon boiling, stir the sugar into the tomato mixture and return to a full rolling boil. Allow to cook at a full boil for 1 minute while stirring. Remove from heat and skim any foam off the surface of the mixture.

Sterilize the jars and lids in boiling water for at least 5 minutes. Pack the tomato jam into the hot, sterilized jars, filling the jars to within 1/2 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 5 minutes.

Remove the jars from the stockpot and place several inches apart onto a cloth-covered or wood surface; allow to sit until cool or overnight. Check the seal by pressing the top of each lid with a finger (the lid should not move up or down at all).