Preheat your grill or grill pan to medium-high heat.
In a small bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, chopped dill, and chopped parsley to create the marinade.
Pat the salmon fillet dry with a paper towel and season both sides with sea salt and black pepper.
Brush half of the lemon-herb mixture over the salmon and the other half over the trimmed asparagus spears.
Place the salmon on the grill skin-side down and cook for 4 to 5 minutes without moving it to ensure a good sear.
Place the asparagus on the grill next to the salmon, turning occasionally until tender and slightly charred, about 5 minutes.
Carefully flip the salmon and cook for another 2 to 3 minutes until the fish is opaque and flakes easily with a fork.
Remove the salmon and asparagus from the grill and serve immediately while hot.