Preheat your grill or a heavy grill pan over medium-high heat until very hot.
In a small bowl, whisk together the olive oil, lemon juice, minced garlic, and finely chopped fresh dill to create the marinade.
Pat the salmon fillet dry with a paper towel and season both sides evenly with sea salt and black pepper.
Trim the woody ends off the asparagus spears and lightly toss them with a small spoonful of the lemon-herb marinade.
Place the salmon on the grill skin-side down and cook undisturbed for 4-5 minutes to develop a nice crust.
Add the asparagus to the grill alongside the salmon, turning the spears occasionally until they are tender and slightly charred.
Carefully flip the salmon and grill for another 3-4 minutes until the internal temperature reaches 145°F and it flakes easily.
Remove everything from the heat, drizzle the remaining lemon-herb marinade over the salmon, and serve immediately.