Preheat oven to 375 degrees. Butter and flour madeleine pans carefully. Melt butter and let it cool.
In the bowl of an electric mixer fitted with the whisk attachment, whisk eggs, sugar and salt together until thick, about 8 minutes. Add vanilla and lemon zest. Using a rubber spatula, fold in flour, rapidly but gently. Fold in butter gently, but make sure it does not settle to bottom. Quickly spoon mixture into prepared madeleine pans. Bake until golden, about 7 minutes. Remove from pans. Cool on racks.