This method will work to dry many fruits and vegetables, but unless you live in the Southwest, forget sun‐drying. Fortunately, the oven does a great job, as long as you don't forget about them. Season the tomatoes as they cook by using more olive oil or adding a variety of fresh herbs or crushed garlic. Use the tomatoes as a garnish with lightly sauced fish or chicken dishes, or—more likely, at least in my house—eat them like candy.
Peel the tomatoes. Cut them in half and scoop out the seeds. Line a baking sheet with aluminum foil and turn the oven to 175F, or a little higher.
Brush the foil with some of the olive oil and arrange the tomatoes, cut side down. Sprinkle lightly with salt and the remaining oil. Place in the oven and forget about them for 2 hours.
Turn the sheet back to front and see how the tomatoes are doing. You have several choices about determining doneness. If you just want to intensify the tomato flavor and use them immediately, they're done when still soft but somewhat shriveled, 2 to 3 hours total. If you want to keep them for a few days, they're done when they're shriveled and mostly dry, at least 4 hours total (wrap and refrigerate). If you want to keep them for weeks, they're done when they're dark, shriveled, and dry, 6 or more hours total (wrap and refrigerate, or store in a jar in the pantry).