Preheat your grill or grill pan to medium-high heat.
Mince the garlic clove and finely chop the fresh dill.
In a small bowl, whisk together the olive oil, minced garlic, chopped dill, and the juice from half of the lemon.
Trim the woody ends off the asparagus spears.
Brush the herb and oil mixture generously over the salmon fillet and the asparagus.
Season both the salmon and asparagus with the sea salt and black pepper.
Place the salmon on the grill skin-side down and cook for 4 to 5 minutes.
Add the asparagus to the grill alongside the salmon.
Carefully flip the salmon and grill for another 2 to 3 minutes until it flakes easily with a fork.
Continue grilling the asparagus for 4 to 5 minutes, turning occasionally until tender-crisp with light char marks.
Remove from heat and serve immediately with an extra squeeze of lemon if desired.