In a mixing bowl, combine the olive oil, minced garlic, chopped basil, chopped parsley, lemon juice, salt, and black pepper to make the marinade.
Place the salmon in the bowl or a shallow dish and pour the marinade over it, turning to coat evenly. Marinate for 20 minutes.
Preheat a gas grill to medium heat (about 350°F / 176°C). Oil the grill grates if needed to prevent sticking.
Remove the salmon from the marinade, letting excess drip off, and place it skin-side down on the grill at a 45° angle for grill marks.
Grill the salmon undisturbed for 4 minutes, then flip and grill the other side for an additional 4 minutes, basting once with remaining marinade while grilling.
If the salmon has charred but is not cooked through, move it to indirect heat, close the lid, and cook 1–2 minutes more until the center is opaque and flakes easily.
Remove from the grill and serve immediately with lemon wedges.