Pat the sockeye salmon fillets dry with paper towels to remove excess moisture.
Season both sides of the salmon fillets evenly with kosher salt and freshly ground black pepper.
Heat a large non-stick skillet over medium-high heat and add the olive oil.
Once the oil is hot and shimmering, place the salmon fillets skin-side down in the skillet.
Cook the salmon without moving it for 4 to 5 minutes, until the skin is crisp and the salmon is cooked about two-thirds of the way through.
Carefully flip the fillets over using a spatula 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.