Preheat the oven to 180 degrees C. Grease or line muffin tins.
In a mixing bowl, cream butter and sugar. Beat in eggs, one at a time. Add lime zest and vanilla; mix well.
Combine flour, bicarb, baking powder and salt. Add to creamed mixture alternately with sour cream (batter will be thick).
Fill each muffin tin about 2/3 full of the mixture. Bake in the preheated oven for 25 to 30 minutes or until a skewer inserted near the centre comes out clean. Cool for 10 minutes; remove to wire racks to cool completely.
To make the lime icing, cream butter and sugar in a small mixing bowl. Add lime juice, vanilla, lime zest and milk; beat until smooth. Ice the cupcakes when they are completely cooled. Sometimes I like to sprinkle toasted coconut on top for a tropical feel. Enjoy!