Combine first 3 ingredients in a 2-quart saucepan. Bring to a boil. Cover, reduce heat, and simmer 30 minutes. Uncover; increase heat to medium, and cook 10 minutes or until ginger is very tender. Remove pan from heat; cover and let stand 30 minutes.
Strain ginger mixture through a sieve into a bowl. Discard solids. Stir in honey until blended. Cover and refrigerate 2 hours or until thoroughly chilled.
Place 4 tablespoons ginger syrup in each of 6 chilled glasses. Stir 3/4 cup seltzer into each glass. Add ice, and serve immediately.