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.
Trim the woody ends off the asparagus and place them in a shallow dish.
Brush the salmon and the asparagus spears generously with the lemon-herb mixture.
Place the salmon on the grill skin-side down and cook for 4-5 minutes without moving it to ensure a good sear.
Place the asparagus on the grill alongside the salmon, turning occasionally to get even char marks.
Carefully flip the salmon and grill for another 3-4 minutes until the internal temperature reaches 145°F and the asparagus is tender.
Remove from the grill and let the salmon rest for 2 minutes before serving.