Fill clean, pre-warmed mason jars, up to half-gallon size, with tart cherry juice, leaving ¼ inch headspace.
Wipe jar rims with a paper towel wetted with white vinegar. Place on lid and screw ring to fingertip tightness.
Place jars in a water bath canner, fill with water until submerged by 1-2 inches of water. Bring to a boil. Once water is boiling, start the timer. For jar sizes up to one litre / one quart, processing time is five minutes. For half-gallon sizes, processing time is ten minutes. If the water ever stops boiling, bring to a boil again and restart the timer. For elevations of 1,001-6,000 feet, add five minutes to processing time.
When process time is up, remove pot from heat and let sit an additional five minutes.
Using a jar lifter, carefully remove jars from canner and place on a thick towel on a counter or table and let sit undisturbed overnight.
The next morning, check if jars have sealed (lid is depressed), and store in a cool dark place for up to a year. If jars have not sealed, place in the fridge and consume promptly.
Notes
While there are no lab-tested recipes specifically for tart cherry juice, this information from Oregon State University Extension Service lays out guidance for safely canning fruit juice and specifically names cherries as an example. While this post is about tart cherries, sweet cherries are within the safety range for canning (a pH of lower than 4.6), but a quick check with a pH testing strip is always recommended.
Keyword nanking cherry juice, sour cherry juice, tart cherry juice