(Note: This trick only works for Majoras Mask on the Legend of Zelda: Collectors Edition disc.)
If you have a game saved at an owl statue, you can keep it without having to create a backup copy of the data. When you get to the file selection screen, remove the memory card from the GameCube. Load the game data and choose to continue without saving. When you save the game at either an owl statue, or by using the Song of Time, it will tell you the data cannot be saved. Reinsert the memory card into the GameCube at that point and it should save.