Place the strawberries, ginger, sugar, and water in a medium-large pot. Bring to a rolling boil on high heat (which takes about 12-14 minutes) then reduce the heat to medium. As the mixture simmers it should be frothy with lively bubbles but not boiling over. Continue to simmer for 8-10 minutes.
Remove the pan from the heat and spoon off any excess foam that may be present.
Set aside on a rack to cool for at least one hour. Using a fine meshed sieve, strain out the solids from the syrup.
Funnel the syrup into a sterilized bottle, or pour it into a jar with a tight-fitting lid. Strawberry syrup will keep in the refrigerator for up to one month.