Remove the sockeye salmon fillets from the refrigerator and pat them dry with paper towels.
Season both sides of the salmon fillets evenly with kosher salt and freshly ground black pepper.
Heat the olive oil in a large non-stick skillet over medium-high heat until shimmering.
Place the salmon fillets skin-side down in the hot skillet. Press down gently with a spatula to ensure even contact with the pan.
Cook the salmon without moving it for 4 to 5 minutes, until the skin is crispy and the salmon is cooked about two-thirds of the way through.
Flip the salmon fillets carefully and add the unsalted butter to the skillet.
Cook for an additional 2 to 3 minutes, spooning the melted butter over the salmon to baste it, until the salmon is opaque and flakes easily with a fork.
Remove the salmon from the skillet and transfer to serving plates.
Serve immediately with lemon wedges on the side for squeezing over the salmon.