Rinse and drain the fresh blackberries and then mash them in a large mixing bowl. Any lumps of fruit that remain will be in your jam, so keep mashing until it reaches a texture you prefer. Add the sugar and lime zest and juice to the bowl. Stir them together and let them sit for 10 minutes.
Meanwhile, wash and dry 8 1-cup containers in hot soapy water. Set them out for filling with jam.
In a small saucepan, combine the pectin and water. Heat over high heat and bring to a boil while stirring constantly. Once it comes to a boil, continue to cook for 1 minute.
Quickly pour the water and pectin into the bowl with the blackberries. Stir the jam together for 3 minutes or until the sugar is mostly dissolved.
Ladle the jam into your prepared containers being sure to leave 1/2-inch space at the top for the jam to expand once frozen. Seal the containers with the lids and let them stand on your counter at room temperature for 24 hours. Freeze the jam for up to one year or place it in the fridge for immediate use.