Divide the ginger, lime, lime leaves and agave nectar between the glasses and muddle well until all the lime juice and flavours from the ginger and lime leaves have been extracted.
Fill each glass to the top with crushed ice and place a straw in each glass. Divide the kombucha between the glasses. Place a large spoon upside down with the tip touching the inside of the glass and float the rum on top by pouring it gently over the spoon.
Garnish with a few extra lime leaves and lime wedges.