Cut fillets lengthwise to separate smaller and larger portions, then pat dry and season with pepper. Wrap each piece of fillet crosswise in a slice of prosciutto, leaving ends of fillet exposed if necessary and tucking 1 or 2 sage leaves between prosciutto and fillet (use 1 leaf for smaller pieces of fish).
Heat 2 teaspoons oil in a 12-inch heavy nonstick skillet over moderately high heat until hot but not smoking, then sauté the 4 larger pieces of fish 4 minutes. Turn over and sauté until just cooked through, about 3 minutes more. Transfer to a platter and keep warm, loosely covered with foil. Wipe skillet clean and heat remaining 2 teaspoons oil, then sauté the 4 smaller pieces of fish, turning over once, until just cooked through, about 4 minutes total.