Preheat a gas or charcoal barbecue to a moderately hot temperature, about 375°F.
Season the insides of the fish with plenty of salt and pepper. Stuff with lemon slices, garlic, cherry tomatoes, and herb sprigs; drizzle the stuffing with 2 Tablespoons oil. Tie the fish at intervals using kitchen string.
When the grill is ready, brush the grates with some oil. Rub or drizzle the outsides of the fish with the remaining 2 Tablespoons oil.
Place the fish on the grill and cook, turning once, until the skin is golden brown and the flesh is just cooked through, 6-7 minutes per side.
When ready, remove from the grill and let cool briefly before serving.
