Bring first 5 ingredients to a boil in a large saucepan. Add pectin, and bring to a full rolling boil. Boil 1 minute. Remove from heat. Remove and discard basil leaves; skim off any foam.
Pour hot mixture immediately into hot, sterilized jars, filling to 1/4 inch from top. Remove air bubbles; wipe jar rims. Cover at once with metal lids, and screw on bands.
Process in boiling-water bath 5 minutes.
Southwest Jelly: Add 1 seeded and thinly sliced jalapeño pepper, and substitute 1 cup cilantro leaves for 1 cup basil leaves. Substitute 20 drops red liquid food coloring for 6 drops of green food coloring.
Mint Jelly: Substitute 1 cup mint leaves for 1 cup basil leaves.
Note: Jellies usually require only 5 minutes of processing because of their higher acid content.