Place the sugar, corn syrup, and water in a 2-quart heavy-bottomed saucepan over medium-high heat. Insert a candy thermometer and cook the sugar mixture until it reaches 311 degrees F, or what is known as the "hard crack" stage. Remove from the heat and carefully pour into a medium-sized, microwave-able glass bowl.
Wash, dry, and lightly but thoroughly coat with cooking spray a clean, dry bowl that matches the diameter of whatever you're placing the sugar cage over. Dip the tines of a fork into the hot sugar. Carefully but quickly wave the fork over the inside of the bowl, allowing the sugar to drip off the fork in long, thin strands. Try to distribute the strands evenly on the sides and bottom of the bowl, making sure to come all the way to the rim, however, not so thick that you can't see the bowl through the sugar.
Using a sharp chef's knife, slice the edge of the cage clean by scraping the blade of the knife along the rim of the bowl. Set aside to cool, about 5 minutes.
To unmold the cage, place your thumbs on the outside of the bowl and your fingers on the inside of the sugar cage. Gently pull the cage loose from the side and bottom of the bowl; you will be able to see the cage release from the inside of the bowl. You will need to apply this gentle pressure all around the inside of the bowl. Once the cage has released from the bowl, carefully lift it out and place it over the dessert. If the sugar is still too warm, the cage may begin to collapse. A good idea is to release the cage from the bowl but leave it in the bowl until it has cooled completely. This will ensure that it keeps its shape. (At this stage, the cage can be stored, right side up, in an airtight container in a cool, dry place for one to two days.)