In a large saucepan, bring water and basil to a boil. Remove from the heat; cover and let stand for 10 minutes. Strain through cheesecloth and discard basil. Return 3-2/3 cups liquid to the pan. Stir in pectin and food coloring. Return to a rolling boil over high heat. Stir in the sugar. Boil for 1 minute, stirring constantly. Remove from the heat and skim off foam.
Carefully ladle hot mixture into sterilized hot half-pint jars, leaving 1/4 inch headspace. Remove air bubbles, wipe rims and adjust lids. Process for 15 minutes in a boiling-water canner. Makes 6 half-pints.