In a small bowl, combine olive oil, lemon zest, lemon juice, chopped dill, chopped parsley, minced garlic, salt, and black pepper. Stir well to mix all ingredients thoroughly.

Place salmon fillets on a plate or in a shallow dish. Evenly spread the prepared marinade over both sides of each salmon fillet, ensuring they are well coated.

Let the salmon marinate for at least 15 minutes at room temperature, or cover and refrigerate for up to 30 minutes for a deeper flavor.

Ensure your grill grates are clean; lightly oil them to prevent the salmon from sticking during cooking.

Place the marinated salmon fillets, skin-side down (if applicable), on the preheated grill. Cook for 4-6 minutes per side, or until the salmon is flaky and cooked through.

Once cooked, carefully remove the salmon from the grill and let it rest for a few minutes before serving. This allows the juices to redistribute, ensuring a moist and flavorful result.