Rinse and drain the blackberries. In a large mixing bowl, combine the blackberries, lemon juice, water, and sugar.
Let the bowl sit at room temperature for at least two hours. I sometimes let the berries sit all day. This helps the sugar to dissolve.
When you are ready to start making the syrup, put the jars in the canner to heat and begin heating the lids in a pan of water on the stove.
Scrape the blackberry mixture into a large stockpot or skillet and begin heating over medium-high heat.
Bring to a boil, stirring constantly, and boil for six minutes.
To separate the seeds from the liquid syrup with no mess, have the fine-mesh sieve placed over a medium saucepan. Pour the hot syrup into the sieve. Press the seeds with a wooden spoon and move them around to make sure the holes in the mesh are not blocked. The liquid will drain into the saucepan. I usually spend 3-5 minutes pushing the blackberry seeds around in the sieve to collect as much liquid as possible in the saucepan.
Let the syrup continue dripping into the saucepan while you get the hot jars in place. When the dripping has stopped, set the mushy seed mixture aside.
Using tongs, if you have them, lift hot jars out of hot water. I usually place mine in the sink. Next to the sink, I place my trusty wooden breadboard. You can use a cutting board or something similar to protect your counter. Put the saucepan of hot syrup on the board and place it next to the jars.
Ladle hot syrup into jars, leaving 1/4 inch headspace. Once all jars are filled, wipe jar rims. Place lids on jars and place bands on jars. Adjust until they are fingertip tight.
Place jars (using a jar-lifter, if you have one) in the hot water bath in the canner. Water should cover the jars by at least one inch. Bring the water to a boil and process the jars for 15 minutes, adjusting for altitude.
When processing is done, remove the jars (again using a jar-lifter, if you have one) and place them on a towel to absorb the drips and to cool.
f all has gone as it should, you should hear the jars seal as they cool. When they are cool, press the center of each lid. They should not flex. Label and store the jars in a cool, dry place. The quality is best if used within one year. Refrigerate any jars once opened.
There are about 40 calories in a tablespoon serving of this recipe for blackberry syrup.