Remove the stems from the mirabelle plums, rinse them, and rinse the raisins separately. Distribute the plums and raisins evenly among clean glass jars. Pour the rum over the fruit until just covered. Let steep at room temperature for 8 hours or overnight.
In a pot, combine the sugar, the carnations, and hot water. Bring to a boil over medium-high heat, stirring occasionally until the sugar dissolves completely. Once at a rolling boil, let it boil for 2 minutes.
Pour the hot syrup evenly into each jar over the fruit and rum, filling to the rim. Immediately seal each jar tightly with its lid.
Place the sealed jars in a large pot or canner and add enough hot water to reach halfway up the sides of the jars. Heat the water to 90°C (194°F) and maintain this temperature for exactly 30 minutes.
Carefully remove the jars from the water bath using a jar lifter or tongs. Set them on a clean cloth and allow to cool completely at room temperature, undisturbed, for 2 to 3 hours. Store in a cool, dark place.