Pat the salmon fillets completely dry with paper towels. Let them sit at room temperature for 15 minutes prior to grilling.
In a small bowl, whisk together the olive oil, juice of one lime, minced garlic, chopped dill, chopped parsley, kosher salt, and black pepper.
Lightly brush the flesh side of the salmon with the herb and lime marinade. Avoid getting the skin wet to ensure it crisps properly.
Preheat your grill to medium-high heat (about 400°F). Clean the grates thoroughly and generously oil them to prevent the fish from sticking.
Place the salmon fillets on the grill skin-side down. Close the lid and cook undisturbed for 6 to 8 minutes, until the skin is crispy and releases naturally from the grates.
Gently flip the salmon using a thin spatula and cook the flesh side for 1 to 2 minutes, or until the internal temperature reaches 125°F for medium doneness.
Remove the salmon from the grill, let it rest for 5 minutes, and serve hot with the remaining lime wedges.