Preheat your grill or a heavy grill pan over medium-high heat.
In a small glass bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, chopped dill, and chopped parsley.
Brush half of the herb marinade over the salmon fillet and season with half of the sea salt and black pepper.
Trim the woody ends off the asparagus and toss the spears with the remaining herb marinade and the rest of the salt and pepper.
Place the salmon on the grill, skin-side down, and cook for approximately 4 to 5 minutes without moving it to ensure a good sear.
Arrange the asparagus spears on the grill next to the salmon, turning them occasionally to get even char marks.
Carefully flip the salmon and grill for an additional 3 to 4 minutes until the internal temperature reaches 145 degrees Fahrenheit and the fish flakes easily with a fork.
Remove the salmon and asparagus from the heat and serve immediately while hot and vibrant.