To make Simple Syrup, mix sugar and water in 1-quart saucepan. Heat to boiling over medium-high heat, stirring until sugar is dissolved. Remove from heat; let stand 30 minutes. Transfer to storage container. Cover and refrigerate up to 3 days. Makes 1 1/4 cups.
To make margarita, add 4 cucumber slices and sprigs of cilantro to cocktail shaker; break up with muddler or spoon. Add 3/4 oz of the simple syrup, the tequila, orange-flavored liqueur and lime juice. Fill shaker with ice; cover and shake vigorously. Strain into cocktail glass filled with fresh ice. Garnish with additional cucumber slices.