Preheat your grill or grill pan to medium-high heat and lightly oil the grates to prevent sticking.
In a small bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, chopped dill, parsley, sea salt, and black pepper.
Place the salmon fillet and trimmed asparagus spears on a tray and brush both sides generously with the herb marinade.
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.
Add the asparagus spears to the grill alongside 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 asparagus is tender-crisp.
Remove from the heat and let the salmon rest for 2 minutes before serving with a final squeeze of fresh lemon if desired.