1) Season tomatoes with the salt and place seed-side down on a rack or paper towel to drain for about 30 minutes. Blot dry with a paper towel.
2) Position an oven rack in the upper part of the oven and preheat the griddle. Line a griddle pan with foil. Place the tomato halves on the prepared pan, seed-side up, season with pepper to taste, drizzle with olive oil, and sprinkle herbs over the top. Grill until hot and the tops begin to brown, about 8 minutes.
3) Top with cheese and cook until cheese is melted, about 1 minute. Serve 3 halves per person.