Prepare your jars and lids. If you wish to make the cherries shelf-stable, please also prepare your canner.
Place a stainless steel or non-reactive stock pot over medium-high heat; add the sugar and water to the pot and stir to dissolve the sugar. Bring the syrup to a boil and add all of the cherries immediately. Return to a boil while stirring constantly. Reduce the heat and allow to remain at a gentle boil for 5 minutes. Turn off the heat.
Using a slotted spoon and a wide-mouthed funnel, transfer the hot cherries from the hot syrup into the jars, leaving 1/2 of an inch of head space (the space between the rim of the jar and the food). Add 1 1/2 Tablespoons of Golden Rum to each jar, then spoon or ladle the hot cherry syrup into the jar, maintaining the 1/2 of an inch of head space.
Insert a chopstick or skewer down the insides of the jar to remove air bubbles. If necessary, add more cherry syrup to keep that 1/2 of an inch of head space.* Wipe the rims of the jars, center the lids on the jars and screw down the rings until finger-tip tight.
*Hang on to that leftover hot syrup and leave it in the pan; that’s the most important part of the Boozy Cherry Molasses! You can either make the Boozy Cherry Molasses right away, or pop the pan into the refrigerator to complete later.
You can either refrigerate the cherries in the syrup for up to a month or you can process them in a boiling water canner to make them shelf stable for a year. I prefer to can them.
To process them, place the jars in a stockpot or canner, covering them by 1-2 inches of warm tap water. Cover the pot and bring to a boil. When the water is at a rolling boil (a boil that cannot be stirred down), begin timing and allow to process for 10 minutes. After 10 minutes, remove the lid to the pot, turn off the heat, wait 5 minutes and then lift the jars straight from the water and place them carefully on a cooling rack positioned over a towel. Do not tilt the jars (it interferes with the natural formation of a vacuum which is one of the things that keeps the food safe and shelf-stable!)
Cool, undisturbed, for 24 hours. As the jars cool, you will hear a popping sound. That is the sound of the lids sealing. That is what you want to hear. Check the jars after 24 hours. If any of them have not sealed, simply store in the refrigerator. Wipe the jars clean and label them before storing in a cool, dry place (like a cupboard.)