Combine the water, honey and ginger in a small saucepan.
Bring the mixture to a boil.
Turn the heat off and let the mixture steep for 10 minutes.
Strain the syrup and let it cool.
Combine the colled syrup and lemon juice in a pitcher.
Fill 4 tall glasses with ice and divide the giner-lemon mixture among them. Top each glass off with sparkling water and garnich with mint sprigs and lemon sedges.