Make the soup: Working in 2 batches, puree cantaloupe, sour cream, honey, lemon juice, and salt in a blender until smooth. Press through a fine sieve into a bowl. Refrigerate until cold, about 1 hour.
Make the syrup: Bring sugar and 3/4 cup water to a boil in a saucepan, stirring until sugar has dissolved. Boil until syrup has reduced to 2/3 cup, about 7 minutes. Remove from heat; add tarragon. Transfer to a bowl; refrigerate until cold, 1 hour.
Puree syrup, tarragon, and lemon juice in a blender until smooth. Refrigerate until ready to use; stir just before serving.
Divide soup among bowls. Drizzle with tarragon syrup; garnish with cantaloupe wedges and tarragon sprigs.