Preheat your oven to 350 degrees F.
Grease 2 (12 cup) muffin pans.
In a small saucepan over medium heat, melt butter. Add brown sugar and rum. Bring to a gentle boil and cook for approximately 2 minutes (stirring often), or until thickened. Remove from heat.
Spoon brown sugar mixture evenly into cupcake tins. Place half of a maraschino cherry in the center of each muffin section. Surround with pineapple tidbits.
In a large bowl, beat cake mix, pineapple juice, eggs and oil on low speed for until moistened, about 30 seconds. Beat on medium speed for 2 minutes.
Spoon cake batter over pineapple, filling almost to the top of each tin (mine were about ⅞ full).
Bake 18 to 22 minutes, or until toothpick inserted in the center is removed clean.
Immediately invert onto wire racks and allow to cool.