Combine all ingredients in the bowl of a food processor and process briefly to break up the seeds. Transfer to a 1-quart Mason jar and set the jar aside for 3 days in a cool, dark place, but don't refrigerate.
Strain the contents through a fine sieve into a 4-cup glass measuring cup. Allow the liquid to drip through; this could take up to 30 minutes.
Transfer the strained liquid to a medium-size nonreactive saucepan. Bring just to a boil over low heat, about 10 minutes.
Remove from the heat and cool to room temperature before using. Store the Grenadine in the refrigerator, where it should keep for up to 6 months.