Generously salt the tops of fish fillets. They'll likely have skins on the bottom so you can leave those alone. Add flour to a long shallow dish. Coat the meaty side of the fish with flour and shake off excess, again, leaving the skin bare.
In a large skillet, heat olive oil over medium heat until rippling. Gently add the fillets, skin side up, to the pan. Cook for about 3 minutes on medium heat. Turn the fillets over, skin side down. Cook for another 2-3 minutes. After the fish is cooked through, using a spatula, carefully remove fillets to the plate. Turn the pan down to medium-low.
Add capers, diced garlic, and lemon juice to the same pan with oil. Cook on medium-low heat for about 1 minute, until garlic softens a bit. Remove from heat. Add 2 tablespoons of butter, off heat, to the caper sauce, stirring, until butter melts and forms a creamy mixture.
Add fish back to the pan, spoon sauce over the fish and serve.