Pre-heat your gas or charcoal grill to cook over medium-high heat. Use a basting brush to coat the cut sides of the tomatoes with olive oil (it will help them not stick so much to the hot grill).
Grill the tomatoes with the cut side down until that surface is charred, 2 to 3 minutes. Use tongs to gingerly (don’t squish them!) transfer the grilled tomatoes to a platter, with the cut side facing up.
Drizzle the tomatoes with the smallest amount of Saba and Fleur de Sel before serving immediately.