In a small saucepan, warm 1 cup of the white grape juice with the rosemary sprigs and honey over medium-low heat until small bubbles form around the edge, about 5 minutes. Do not let it boil.
Remove from heat and let the rosemary steep in the warm liquid for 15 minutes, until it smells strongly herbal.
Strain out the rosemary sprigs and let the syrup cool to room temperature.
In a large pitcher, combine the cooled syrup, the remaining 3 cups of grape juice, and the lemon juice. Chill for at least 1 hour.
Pour the chilled base into a punch bowl or pitcher and add the club soda just before serving, stirring once gently.
Garnish with halved grapes and small rosemary sprigs floated on top.
Good to Know
The rosemary syrup keeps for about a week in the fridge, so make a double batch and use the rest in lemonade or iced tea later in the week.