Preheat oven to 350°F and set aside three to four non-stick madeleine pans.
Combine sugar and eggs in a bowl and mix on medium-low speed using an electric hand-held mixer. Mix until slightly foamy.
Add flour and baking soda; mix until combined. Mix in melted butter and vanilla. Fold in blueberries.
Add about 1/2 tablespoon of batter (making sure to get a few blueberries in each) to each of the shell-shaped cavities in the Madeleine pans. Bake for 5-7 minutes, or until edges are golden brown and the "bump" in centers of madeleines are set.
Let the madeleines cool in the pans for a few minutes, then gently remove them from the pans with a knife and let them finish cooling on a wire rack. Repeat with remaining batter.