Trim and discard ends from oranges. Cut fruit crosswise into 1/4-inch-thick slices, discarding seeds. Put fruit in a 5- to 6-quart pan. Add pineapple juice, ginger, and sugar. Bring to a boil on high heat; cover and simmer on low heat to blend flavors, about 15 minutes.
Add dry white wine and Muscat wine; heat until steaming, about 5 minutes. Do not boil.
Keep punch warm over lowest heat; ladle into cups.