Melt butter in a large flat skillet or chafing dish; add sugar, and cook over medium heat until bubbly. Add banana halves; heat 2 to 3 minutes, basting constantly with sauce. Sprinkle with cinnamon. Remove from heat, and set aside.
Place rum and liqueur in a small, long-handled pan; heat just until warm. Pour over bananas, and ignite with along match. Baste bananas with sauce until flames die down. Serve immediately over ice cream.