Do not twist or wring doilies while they are wet, and use sewing needles or pins to tack the doily into the desired shape while drying. Do not let the stiffening mixture boil, and allow the doily to dry undisturbed in a clean area for at least a day.
To make a stiffening solution, heat 1/2 cup water and 1 1/2 cups of sugar to a low simmer, and cook until mixture is clear. Wet doilies in very warm water, and blot to remove excess water. Soak the doilies in the sugar mixture for a minute or two, then gently press each doily to remove excess solution. Dry doilies flat on a clean, dry towel.