Heat the oven to 350°F (175°C) and line a 12-cup muffin pan with paper liners. Zest the lemons and limes before squeezing them, taking only the colored outer peel and avoiding the bitter white pith.

Whisk the flour, baking powder, baking soda, and salt together in a medium bowl. In a separate bowl, beat the softened butter and granulated sugar for 2–3 minutes, until light and fluffy.

Beat in the eggs one at a time, allowing each to incorporate before adding the next. Mix in the lemon zest, lime zest, lemon juice, lime juice, and vanilla extract.

Add the dry ingredients in two or three additions, alternating with the room-temperature buttermilk. Mix only until combined, since overmixing can make the cupcakes tough or dense.

Divide the batter evenly among the liners, filling each about two-thirds full. Bake for 18–22 minutes, until the tops spring back lightly and a toothpick comes out clean or with a few moist crumbs.

Cool the cupcakes in the pan for 5 minutes, then transfer them to a rack and cool completely. For the buttercream, beat the softened butter until smooth, gradually add the sifted confectioners’ sugar, then mix in the citrus juices, zests, and salt; add cream or milk gradually until fluffy and spreadable.

Pipe or spread the buttercream over the completely cooled cupcakes. Finish with thin lemon or lime zest, small citrus wedges, or candied citrus peel if desired.