Preheat your grill to a high heat, ensuring the grates are hot and lightly oiled to prevent sticking.
Pat the salmon fillets dry with paper towels, then brush the flesh side lightly with olive oil and season generously with salt and pepper. Keep the skin on for crispy texture.
Place the salmon fillets skin-side down onto the hot grill. Hear the sizzle and see the skin crackle as it makes contact with the grates. Grill for about 4-5 minutes, until the skin is crisp and golden brown.
Meanwhile, trim the asparagus ends and toss the stalks with a little olive oil and a pinch of salt. Arrange them directly on the grill grates alongside the salmon.
Flip the salmon carefully using tongs, cooking for another 3-4 minutes until the fish is opaque and flakes easily, and the asparagus begins to char slightly and blister in spots.
Remove the salmon and asparagus from the grill once they reach your desired doneness—salmon should be tender and flaky, asparagus tender yet slightly crisp and smoky.
Squeeze fresh lemon wedges over the hot salmon and asparagus to add bright flavor that cuts through the smoky richness. Serve immediately for the best texture and aroma.