Prepare storage jars with tight-fitting lids by sterilizing in a hot water bath. Remove from the bath using tongs and allow to dry completely.
Line a large rimmed baking sheet or sheets with parchment paper. Place a drying rack over the parchment.
Preheat the oven to 250° F, or the lowest setting possible.
Cut each tomato in half lengthwise. If using any tomato larger than a cherry tomato, scoop the seeds and pulp out and discard.
Once all of the tomatoes have been sliced, place each tomato half, cut side up, on the drying rack leaving room between each and every tomato. Nobody should be touching.
Sprinkle the tomatoes lightly with the flaked sea salt.
Place baking sheet in the oven. Bake for 2.5 to 3.5 hours, or until the tomatoes are dehydrated and leathery, but not crispy. Check them every hour during drying.
Remove from the oven and allow to cool. To store, transfer the sun-dried tomatoes to a jar or jars. If using garlic or herbs, tuck these in and around the tomatoes as you pack them. Pack the jars until full, but not too tight. Fill with a quality olive oil until the tomatoes and any extra ingredients are completely covered. Fasten lids and refrigerate for up to 2 weeks. Alternatively, cooled tomatoes may be placed into freezer bags and frozen, without oil or additional ingredients, for up to 3 months.