Preheat your grill to medium-high heat and lightly oil the grates to prevent sticking.
Mince the garlic clove and finely chop the fresh dill and parsley.
In a small bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, dill, parsley, salt, and pepper.
Brush the salmon fillet and the trimmed asparagus spears generously with the prepared lemon-herb mixture.
Place the salmon on the grill, skin-side down, and cook for about 4-5 minutes without moving it.
Arrange the asparagus spears on the grill next to the salmon and cook for 3-5 minutes, turning occasionally.
Carefully flip the salmon and grill for an additional 3-4 minutes until it reaches your desired level of doneness and the asparagus is tender.
Remove the salmon and asparagus from the grill and serve immediately with an extra squeeze of fresh lemon.