Divide the lemon zest and cloves between 2 pint-size canning jars. Carefully divide the blackberries between the jars (you don't want to bruise the fruit).
In a small saucepan, heat the apple cider vinegar, sugar, salt and 1 1/2 cups water over high, stirring until the sugar dissolves. Let cool completely.
Pour the brine over the berries, making sure they're completely submerged. Screw on the lids. Let stand at room temperature 24 hours. Refrigerate at least 3 days before eating. (The pickles are best eaten within 10 days.)