01 - In a small bowl, whisk together the olive oil, lemon juice, lemon zest, dill, parsley, garlic, salt, and black pepper until well combined.
02 - Arrange the salmon fillets in a shallow dish and pour the marinade over them, making sure each fillet is evenly coated. Cover and refrigerate for at least 15 minutes or up to 1 hour for deeper flavor.
03 - While the salmon marinates, combine the Greek yogurt, diced cucumber, dill, chives, lemon juice, salt, and black pepper in a bowl. Stir until evenly mixed, then cover and refrigerate until ready to serve.
04 - Heat an outdoor grill or grill pan to medium-high heat, ensuring the grates are clean and lightly oiled to prevent sticking.
05 - Remove the salmon from the marinade and place the fillets skin-side down on the hot grill. Cook for 4 to 6 minutes per side until the flesh flakes easily with a fork and deep grill marks form.
06 - Transfer the grilled salmon to individual plates. Spoon the cucumber dill sauce generously over each fillet, or serve the sauce on the side alongside lemon wedges.