In a small bowl, combine the olive oil, minced garlic, fresh lemon juice, lemon zest, chopped thyme, chopped parsley, salt, and pepper. Mix well.
Place the barramundi fillets in a shallow dish. Pour the marinade over the fillets, making sure each fillet is well coated. Cover and refrigerate for at least 30 minutes.
Preheat your grill to medium-high heat. If using an oven, preheat to 400°F (200°C).
If grilling, place the marinated barramundi fillets on the grill and cook for about 4-5 minutes on each side, or until the fish is cooked through and flakes easily with a fork.
If baking, place the fillets on a baking sheet lined with parchment paper or lightly greased. Bake in the preheated oven for about 12-15 minutes, or until the fish is cooked through and flakes easily with a fork.
Transfer the cooked barramundi fillets to a serving platter. Serve hot with lemon wedges on the side.
Enjoy your meal!