Preheat the grill to medium-high heat and lightly grease the grates with a small amount of oil.
In a small bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, chopped dill, and chopped parsley.
Season the salmon fillet and the asparagus spears evenly with sea salt and black pepper.
Brush the prepared lemon-herb mixture generously over the top of the salmon and the asparagus.
Place the salmon on the grill, skin-side down, and cook for 5-6 minutes without moving it to ensure a good sear.
Carefully flip the salmon and grill for another 3-4 minutes until the internal temperature reaches 145 degrees Fahrenheit and it flakes easily.
Grill the asparagus alongside the salmon for 4-5 minutes, turning occasionally until tender and slightly charred.
Remove from the heat and serve immediately with an extra squeeze of fresh lemon if desired.