Melt 1 tablespoon of butter in a large nonstick skillet over medium heat.
Season the salmon fillets with about ½ teaspoon salt and ¼ teaspoon pepper. Add to pan and cook until opaque throughout, 3 to 5 minutes per side, then transfer to plates.
Wipe out the skillet and melt the remaining 3 tablespoons of butter over medium heat. Add the almonds and cook, stirring frequently, until the almonds and butter are golden brown, 2 to 3 minutes (be careful not to burn!) Stir in the capers. Spoon over the salmon fillets and serve.