Scald 5 pint jars in a large pot of simmering water fitted with a rack—you will use this pot to process the jars. Right before filling, put the jars on the counter. In a dry sauté pan over medium heat, toast the dill seeds and peppercorns. Divide the spices among the jars, using about 11/2 teaspoons per jar, then add 2 sprigs dill and 1 garlic clove to each jar. Pack the tomatoes evenly among the jars. Meanwhile, soak the lids in a pan of hot water to soften the rubber seal.

In a pot, bring the vinegar, water, sugar, and salt to a boil. Transfer the brine to a heat-proof pitcher and pour over the tomatoes, leaving a 1/2-inch space from the rim of the jar. Check the jars for air pockets, adding more brine if necessary to fill in gaps. Wipe the rims with a clean towel, seal with the lids, then screw on the bands until snug but not tight.

Place the jars in the pot with the rack and add enough water to cover the jars by about 1 inch. Bring the water to a boil and process the jars for 15 minutes (start the timer when the water reaches a boil). Turn off the heat and leave the jars in the water for a few minutes. Remove the jars from the water and let cool completely.