Preheat an oven to 220 degrees C. Toss the crabmeat in the melted and cooled butter. Set aside until ready to serve.
Pat fillets dry and season with salt and pepper. Heat olive oil in large heavy frypan over medium-high heat until hot, but not smoking. Brown filets on both sides, about 3 minutes per side.
Transfer fillets to an oiled baking pan and roast in the middle of the preheated oven until they start to firm and are reddish-pink and juicy in the center, about 10 minutes. Top each fillet with the crabmeat and butter mixture.