In the bottom of an 11- to 12-inch-wide steamer or in a deep 5- to 6-quart pan, combine orange juice, lime juice, and ground ginger. Set a nonstick or oiled rack at least 1 inch above surface of juice (elevate, if necessary, on the rim of a cheesecake pan or three clean, empty 2- to 3-in.-tall cans with both ends removed). Cover pan and bring juice to a boil over high heat.
Rinse fish. Set pieces slightly apart on rack over boiling juice; cover pan and reduce heat to medium. Steam until fish is barely opaque but still moist-looking in center of thickest part (cut to test), 8 to 10 minutes. Lift out rack. With a wide spatula, lift fish from rack and set on a warm plate; cover to keep warm. Increase heat to high and boil pan juices, uncovered, until reduced to about 1 1/2 cups, 10 to 12 minutes.
In a small bowl, mix cornstarch with 3 tablespoons water. Add mixture, along with fresh ginger, to reduced pan juices; stir until boiling. Add salt and cayenne to taste.
Divide sauce evenly among four dinner plates. Lay a piece of fish in sauce on each plate. Garnish each portion with a few drops of chili oil and shreds of lime peel.