Whisk together the egg yolks and lime juice in a stainless steel bowl until they are lighter in color, and thickened. Heat about 2 inches of water in the bottom of a small saucepan to simmering (or use a double boiler). Place the bowl on top of the saucepan, without allowing the water to touch the bottom of the bowl. Be careful not to get the eggs to hot or they will scramble.
Continue whisking the egg mixture rapidly. Slowly drizzle the melted butter into the eggs until the sauce is thick and double in volume. Remove from the heat.
Add the cayenne pepper, salt and cilantro to the sauce. Cover and keep warm until you are ready to serve.