Put egg whites and sugar in the heatproof bowl of an electric mixer set over a pan of simmering water. Whisk constantly until sugar is dissolved and mixture registers 140 degrees on an instant-read thermometer, 2 to 3 minutes.
Transfer bowl to mixer; fit mixer with the whisk. Beat on medium-high speed until mixture has cooled and formed stiff, glossy peaks, 6 to 8 minutes.
Line four baking sheets with waxed or parchment paper; set aside. Fit a pastry bag with a coupler and an Ateco number 13 star tip; fill bag with meringue. For Lord Baltimore cake, pipe 120 1/2-inch-high fleurs-de-lis onto lined sheets, refilling pastry bag as needed; for Lady Baltimore cake, pipe 3/4-inch-high fleurs-de-lis. Let dry overnight.
If humidity is high and meringues remain moist, preheat oven to its lowest temperature (about 150 degrees), and bake meringues until they are dry; do not let them brown. Let cool; wrap sheets with plastic.
Store in a cool, dry place up to 2 weeks.
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