In a small saucepan, bring sugar, ½ cup water, and clementine juice and halves to a boil over medium-high heat. Reduce heat to medium-low; cook until sugar is dissolved and syrup is slightly thickened, about 20 minutes. Remove from heat; cover and let stand for 30 minutes. Strain mixture through a fine-mesh sieve, discard clementine halves. Cover and refrigerate until ready to use.