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.
Trim the woody ends off the asparagus and place them in a bowl, tossing with half of the herb-lemon mixture.
Season the salmon fillet with sea salt and black pepper, then brush the remaining herb-lemon mixture over the top.
Place the salmon on the grill, skin-side down, and cook for 4-5 minutes.
Add the asparagus to the grill alongside the salmon, turning occasionally to ensure even charring.
Carefully flip the salmon and grill for another 3-4 minutes until the fish is opaque and flakes easily with a fork.
Remove both the salmon and asparagus from the heat and serve immediately while hot.