1. To prepare juice: Wash sea grapes and put in a large, wide pot with half as much water (1 cup water to 2 cups sea grapes). Bring to a boil. Mash often with a potato masher and continue boiling until fruit is reduced to a soft pulp (about 25 to 30 minutes). Strain through a several layers of cheesecloth. Do not squeeze.
2. Place one quart of juice in a wide pot. Add lime juice and pectin and bring mixture to a boil. Stir in sugar and return to a boil. Boil for 1 minute, stirring constantly. Remove from heat. Skim foam if necessary. Pour while still hot into hot, sterilized jars, leaving 1/4-inch head space. Adjust caps. Process 5 minutes in boiling water bath.