Combine all of the ingredients in a small saucepan. Bring to a boil on medium heat until the sugar is fully dissolved, about 2 minutes, then cover and bring to a simmer over low heat for 45 minutes.
Pour the cooled syrup through a fine mesh strainer into a glass container.
To Make One Glass of Ginger Ale
Combine the syrup and soda water in a tall glass, and stir to combine. Top it off with ice and a squeeze of juice from the ¼ lime.
Notes
The recipe yields 3 cups of ginger syrup, which is enough to make 24 glasses of homemade ginger ale. One serving of the syrup is 2 tablespoons.Nutritional information is for 1 tablespoon syrup.