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 - Place the salmon fillets in a shallow dish and pour the marinade over them, ensuring 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. Mix thoroughly, cover, and refrigerate until ready to serve.
04 - Preheat an outdoor grill or grill pan to medium-high heat.
05 - Remove the salmon from the marinade and place the fillets skin-side down on the grill. Cook for 4 to 6 minutes per side, until the flesh flakes easily with a fork and develops distinct grill marks.
06 - Transfer the grilled salmon to serving plates. Spoon the cucumber dill sauce over each fillet, or serve it alongside.