Heat oven to 200 degrees and place a large oven-safe plate or baking sheet inside. This is only if you are unable to fit all of the fish in your skillet at once.
Place flour on a large, shallow plate. Season both sides of fish fillets with salt and pepper to taste. Dredge fish in flour, shaking off excess.
In a nonstick skillet, heat half of the clarified butter until bubbling. Place half of the fish fillets in the pan and cook until just done, 2 to 3 minutes per side, then transfer to the plate or baking sheet in the oven to keep warm. Add the other half of the clarified butter to skillet and heat until bubbling, then cook remaining fillets. Wipe out the skillet.
Add the butter to the skillet and heat until bubbling and golden, then pour evenly over fillets. Serve immediately, with lemon wedges on the side.