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 toss the spears with a small drizzle of the lemon-herb marinade.
Brush the remaining marinade generously over the top and sides of the salmon fillet.
Place the salmon on the grill, skin-side down, and cook for 4-5 minutes without moving it to ensure a crisp skin.
Add the asparagus spears to the grill alongside the salmon, turning them occasionally.
Flip the salmon carefully and grill for another 3-4 minutes until the fish reaches your desired doneness and the asparagus is tender with light char marks.
Remove from the heat and serve immediately with an extra squeeze of fresh lemon if desired.