To Make the Syrup: Combine sugar and water in a small saucepan and place over medium heat. Whisk to dissolve the sugar then add thyme. Bring to a simmer and cook, 2 minutes.Remove from heat, cover, and let steep for 1 hour. Strain and chill. Syrup will keep covered in the refrigerator for 1 month.
To make the Margaritas: Rub the lime wedge around the rim of a cocktail glass. Dip glass in salt to coat the edges. Fill glass with crushed ice.Fill a cocktail shaker with ice, add tequila, clementine juice, syrup, and lime juice and shake vigorously. Strain drink into prepared glass and garnish with a thyme sprig.
Notes
Clementines are often called Cuties in the grocery store.