Preheat your grill to medium-high heat (around 375-400°F). Clean and oil the grates well to prevent sticking.
In a small bowl, combine olive oil, lemon zest, lemon juice, minced garlic, salt, and pepper. Pat the salmon fillets dry with paper towels, then brush them with the marinade mixture.
While the grill heats up, prepare the dill sauce by mixing all sauce ingredients in a bowl. Refrigerate until ready to serve.
Place the salmon fillets skin-side up on the grill. Cook for 4-5 minutes until grill marks appear.
Carefully flip the salmon using a wide spatula. Cook for another 3-4 minutes, or until the fish is cooked to your preferred doneness.
Transfer the salmon to serving plates and let rest for 2-3 minutes. Serve with a generous dollop of dill sauce.