Rinse nine 1-cup plastic or freezer-safe containers and lids with boiling water. Dry thoroughly.
In a small bowl, thoroughly crush strawberries, 1 cup at a time, to measure exactly 5 cups; transfer to a 6-qt. stockpot. Stir in pectin, lime juice and butter. Bring to a full rolling boil over high heat, stirring constantly. Stir in sugar; return to a full rolling boil. Boil and stir 1 minute. Immediately stir in basil and lime zest.
Immediately fill all containers to within 1/2 in. of tops. Wipe off top edges of containers; immediately cover with lids. Let stand at room temperature 24 hours.
Jam is now ready to use. Refrigerate up to 3 weeks or freeze up to 12 months. Thaw frozen jam in refrigerator before serving.