1. In a mortar, combine the ginger, chiles and a pinch of salt and pound to a paste. Stir in 2 tablespoons of the oil and transfer to a small bowl. Lay the fish on a work surface, skinned side down. Using a sharp knife, make 3 long, shallow slashes across the grain in each fillet. Rub the fish all over with half of the ginger-chile paste, working some of it into the slashes. Transfer the fish to a platter, cover and refrigerate for 1 hour or overnight. Refrigerate the remaining ginger-chile paste.
2. Arrange the tomato slices on paper towels to drain briefly; pat the tops dry. Lightly brush a nonstick grill pan with oil and set it over moderately high heat. Season the fish with salt and add it to the pan, skinned side up. Grill the fish over moderately high heat until golden and crusty on the bottom, about 5 minutes. Turn the fish, reduce the heat to moderate and cook until the fish is cooked through and the flesh begins to flake, 4 to 5 minutes longer. Transfer the fish to a platter, cover loosely with foil and keep warm.
3. Wipe out the grill pan. Brush the tomatoes with the remaining ginger-chile paste, season with salt and cook in the grill pan over moderately high heat until browned, about 2 minutes per side. Serve the fish with the tomatoes and lime wedges.
Wine Recommendation: This dish has a ginger-chile bite best matched with a tart Sauvignon Blanc-based Bordeaux Blanc, such as the 1998 Château Bonnet Entre-Deux-Mers.