Pre-heat the oven to 175℃ / 350℉.
Line a muffin tin with four large cases (see note 2).
Cream the butter and sugar together until fluffy.
Add the eggs, one at a time, and whisk them into the butter/sugar mixture.
Add the lime juice and whisk in.
In a separate bowl, combine the flour, polenta and baking powder.
Stir in to the wet ingredients, just until everything is combined.
Dollop into the cupcake cases and bake in the bottom part of the oven for around 20-22 minutes (see note 2).
The cupcakes are ready when an inserted skewer comes out almost clean.
Remove from the oven and allow to cool before icing.