Heat 1 tablespoon of the butter in a large nonstick skillet over medium heat. Season the salmon with ½ teaspoon salt and ¼ teaspoon pepper.
Cook the fish until opaque throughout, 3 to 5 minutes per side. Transfer to individual plates.
Meanwhile, fill a second skillet with ½ inch of water, bring to a boil, and add ¼ teaspoon salt.
Add the green beans to the second skillet, cover, and steam until just tender, 4 to 5 minutes. Drain and transfer to plates.
Wipe out the green bean skillet and heat the remaining 3 tablespoons of butter over medium heat.
Add the almonds and cook, stirring frequently, until almonds and butter are golden brown (but not burned), 2 to 3 minutes. Stir in the capers. Spoon over fish and beans.