Combine all ingredients in a wide pot with a tight-fitting lid and stir to combine.
Place lidded pot on the stove over medium-high heat and cook for approximately 20 minutes, until the cherries are fully thawed and the onions are softened. For fresh cherries, cook 20 minutes until the cherries and onions have softened.
Continue to cook, with the lid off, for 5 minutes. If you are using fresh cherries, cook until the mixture has reduced by approximately half.
Remove pot from heat. Using an immersion blender, puree the mixture until smooth (you may have to tip the pan a little in order to do this without splashing). If you don’t have an immersion blender, scrape the mixture into a blender or food processor and blend until smooth.
If the sauce is nice and thick, it is done. If it’s still a little watery, return it to the heat and cook a bit longer. At this point, taste it and add more salt or pepper, if necessary.
When it’s finished, remove the pot from the stove and funnel the finished sauce into the prepared jars. Wipe rims, apply lids and rings and process in a boiling water bath canner for 15 minutes. (Check altitude chart below for adjustments.)