Preheat your grill to medium-high heat (about 400°F/200°C). If using an indoor grill pan, heat it over medium-high heat with a light coating of oil.
In a small bowl, whisk together 1 tablespoon of olive oil, the lemon zest, lemon juice, minced garlic, dill, salt, and black pepper to create a marinade.
Pat the salmon fillets dry with paper towels. Brush both sides of the fillets with half of the marinade. In a separate bowl, toss the asparagus with the remaining 1 tablespoon of olive oil, a pinch of salt, and black pepper.
Place the salmon fillets on the grill, skin-side down if applicable. Grill for 4-6 minutes per side, depending on thickness, until the salmon flakes easily with a fork and reaches an internal temperature of 145°F (63°C). Avoid overcooking to keep it moist.
While the salmon cooks, add the asparagus to the grill. Cook for 4-5 minutes, turning occasionally, until tender and slightly charred. If the grill is crowded, you can cook the asparagus in batches or use a grill basket.
Transfer the grilled salmon and asparagus to a serving platter. Drizzle any remaining marinade over the top or serve with lemon wedges on the side. Enjoy your grilled salmon with asparagus hot off the grill!