Pat the salmon fillets dry thoroughly with paper towels, focusing on removing moisture from the skin to ensure crispiness.
Sprinkle a small amount of coarse sea salt over the skin side of each fillet, then let them sit for about 10 minutes to help draw out excess moisture.
Meanwhile, heat your skillet over medium-high heat until it’s shimmering hot, and the surface is nearly smoking.
Add a tablespoon of high-smoke-point oil to the hot pan and swirl to coat the surface evenly.
Gently place the salmon fillets skin-side down into the pan, away from you to avoid splatters. You should hear an immediate sizzle and see the skin start to crisp and turn golden.
Press each fillet gently with a spatula for about 10 seconds to ensure full contact between skin and pan, which promotes even crackling.
Allow the salmon to cook undisturbed for 4-5 minutes, until the skin is deep golden and crispy, and the flesh is opaque around the edges.
Carefully flip the fillets using a wide spatula, and cook the flesh side for an additional 1-2 minutes until just cooked through.
Remove the salmon from the pan and let it rest for about 2 minutes on a plate; this helps juices settle and keeps the skin crispy.
Squeeze fresh lemon over the fillets and zest a little on top for bright flavor. Serve immediately to enjoy the crispy skin and tender flesh.