To make the simple syrup: In a small saucepan, combine 1/4 cup of water with 1/2 cup of sugar over medium heat. Bring to a boil and stir until all the sugar is dissolved. Take pan off heat and set aside to cool.
For the sugar rims: In a shallow bowl, combine 1/4 cup of sugar with the lemon and lime zest. Rub the lemon around the glass rim, making sure to evenly coat both inside and out. Lightly press the rim into the sugar to frost.
In a small pitcher, combine the Prosecco, amaretto liqueur, lemon juice, and 2 tablespoons of cooled simple syrup. Pour into the sugared glass over ice.
Garnish with a slice of lemon and a slice of lime.