Preheat your grill or a heavy grill pan over medium-high heat.
In a small mixing bowl, whisk together the extra virgin olive oil, lemon juice, lemon zest, minced garlic, fresh dill, dried oregano, sea salt, and black pepper.
Brush half of the prepared herb marinade generously over the salmon fillet and use the remaining half to coat the asparagus spears.
Place the salmon onto the hot grill skin-side down and cook undisturbed for 4 to 5 minutes.
Arrange the asparagus spears on the grill next to the salmon during the last few minutes of cooking.
Carefully flip the salmon and grill for an additional 3 to 4 minutes until the fish is opaque and flakes easily with a fork.
Continue grilling the asparagus, turning occasionally, until they are tender and show light char marks.
Remove both the salmon and asparagus from the grill and serve immediately while hot.