Preheat your grill to medium-high heat and lightly grease the grates with a small amount of oil to prevent sticking.
In a small mixing bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, and finely chopped fresh dill.
Place the salmon fillet and the trimmed asparagus spears on a large tray or plate.
Brush the lemon-herb mixture generously over both sides of the salmon and all over the asparagus spears.
Season the salmon and asparagus evenly with sea salt and freshly cracked black pepper.
Place the salmon on the grill skin-side down and cook for 4 to 5 minutes per side, or until the fish reaches your desired level of doneness and flakes easily with a fork.
Add the asparagus to the grill during the last 4 to 5 minutes of the salmon's cooking time, turning occasionally until they are tender and show light char marks.
Remove everything from the grill and serve immediately while hot, garnished with extra fresh dill if desired.