Lay sardines side by side on a clean, dry kitchen towel or on paper towels and gently roll together into a cylinder to remove excess moisture. Refrigerate until ready to use. (It is very important that the sardines are sufficiently dry before oiling, seasoning, and grilling.)
Preheat a very clean, well-oiled grill or broiler to high.
In a medium mixing bowl, combine diced tomatoes, 1/2 cup olive oil, olives, parsley, basil, cilantro (if using), shallot, and garlic. Add 1 tablespoon lemon juice, 1 teaspoon salt, and 1 /2 teaspoon pepper. Mix well. Set aside at room temperature until sardines are ready to be served.
Transfer sardines to a small rimmed baking sheet and drizzle 1/4 cup olive oil over them. Turn sardines in oil to coat. Oil grill grate one more time before you begin cooking. Season sardines on both sides with 1 teaspoon salt and 1/2 teaspoon pepper. Place directly on grill and cook, undisturbed, until skin is crispy and lightly charred, 2 to 3 minutes. Turn sardines over and cook another 2 to 3 minutes. (If you try to turn the fish too soon, they will stick to the grill. Be patient here and the fish will turn easily once the skin has crisped.)
While fish are cooking, brush lemon slices and tomato halves lightly with remaining 1 /4 cup olive oil. Season with sea salt and black pepper to taste, and place on grill. Grill until softened and nicely marked on both sides, about 2 minutes.
Place tomato mixture on a serving platter, arrange grilled sardines on top, season them a final time with sea salt and black pepper, and drizzle with remaining 1 /4 cup lemon juice and remaining 1 /4 cup olive oil. Serve immediately with the grilled tomato halves and grilled lemon slices.