Mix butter, beaten eggs, honey, pineapple juice, and vanilla extract in a medium bowl and set aside.
Mix flour, baking powder, baking soda, and salt in a medium mixing bowl.
Slowly add dry mixture to wet mixture. Add finely chopped pineapple and mandarin orange segments.
Fill muffin tins 2/3 full and bake for 20 minutes. Check by inserting toothpick and see if it comes out clean.
Makes 15 - 18 muffins.