There are several egg-free meringue recipes, including those found on Slate.com and VeganStreet.com. These recipes use whipped chickpea water, sugar and cream of tartar to replicate traditional egg-based meringue.
To make egg-free meringues, pour the water from a 15-ounce can of chickpeas into the bowl of an electric mixer outfitted with a whisk attachment. Whip the water for 15 minutes, or until the mixture is frothy and holds stiff peaks. With the mixer running, add 1 tablespoon vanilla extract and 1 cup white sugar. Scoop the meringue into a pastry bag, attach a piping tip, and squeeze the meringue into rounds on a baking sheet covered with parchment paper. Bake the meringues for 90 minutes at 250 degrees Fahrenheit.