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 parsley.
Pat the salmon fillet dry with a paper towel and season both sides with sea salt and black pepper.
Brush the herb-lemon mixture generously over the salmon and the asparagus spears.
Place the salmon on the grill, skin-side down first, and cook for 4-5 minutes.
Add the asparagus to the grill alongside the salmon, turning occasionally until tender and slightly charred.
Carefully flip the salmon and grill for another 3-4 minutes until the internal temperature reaches 145°F and the flesh is opaque.
Remove from heat and let the salmon rest for 2 minutes before serving with the grilled asparagus.