Preheat the grill to medium-high heat 400-450°F/200-230°C, and clean and oil the grill grates.
In a small bowl, combine garlic, butter, lemon juice, salt and pepper.
Drizzle the butter mixture over the salmon fillets, and brush to cover the salmon.
Place the salmon fillets on the grill, skin side down over direct high heat. Cover with the lid, and cook for about 6-7 minutes. The color of the salmon will become light as it cooks, and the salmon should be easy to flip without sticking to the grill grates (that’s how you know that it’s ready to be flipped).
Flip the salmon, and cook for 2-4 more minutes or until the internal temp is 130°F/54°C. If needed cook on the sides as well.
Transfer to a plate, and allow to rest for a couple of minutes before serving. Garnish with chopped parsley, and serve with lemon wedges.