Scrub your grill grates down and generously oil them with olive oil. Heat to medium high.
Generously rub the branzino down with olive oil and liberally season with salt and pepper inside and out.
Place the branzino skin side down on a tray, and fill one side with herbs and lime. Fold the second side over on top of the herbs, so the fish are stuffed and back to their regular fish shape (see photographs).
Gently lay the fish on the hot, well-oiled grill and cook without turning for about 5 minutes until the skin is crisp and the the flesh on the grill-side of the fish is flakey and opaque. Use a spatula to loosen the fish from the grill; there may be a spot or two that sticks. Flip the fish over and continue grilling for about 3 to 4 minutes. Remove fish to a serving plate and let rest for 5 minutes before serving.
Drizzle more olive oil and juice from 2 limes over the fish. Serve.