Preheat your grill or grill pan to medium-high heat.
In a small bowl, whisk together the olive oil, lemon zest, lemon juice, minced garlic, chopped dill, chopped parsley, sea salt, and black pepper.
Trim the woody ends off the asparagus and place them in a bowl, tossing with half of the prepared herb-oil mixture.
Brush the remaining herb-oil mixture over both sides of the salmon fillet.
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 until tender and slightly charred.
Flip the salmon carefully and cook for another 3-4 minutes until it reaches your desired level of doneness and flakes easily with a fork.
Remove from heat and serve the salmon immediately with the grilled asparagus on the side.