Add the caraway seeds to a dry saucepan and toast until lightly fragrant, about 1 minute. Add the sugar and 1/2 cup water and bring to a simmer, stirring until the sugar is dissolved. Turn off the heat and let steep until cool. Strain and discard any solids.
Fill a cocktail shaker and 2 rocks glasses with ice. Add the aquavit, orange juice, lemon juice and 2 tablespoons caraway syrup to the shaker and shake vigorously (save the remaining syrup for another use). Pour the drink into the glasses and top with club soda. Garnish with the orange half-rounds.