Bring plums and sugar to a boil in an 8-quart stainless steel or enameled Dutch oven over medium-high heat, stirring often. Reduce heat, and simmer 5 minutes or until plums soften, stirring often. Pour mixture through a colander into a bowl, using back of a spoon to squeeze out juice to measure 4 ½ cups. Reserve 2 cups pulp.

Sterilize jars, and prepare lids.

While jars are boiling, pour reserved 4 ½ cups plum juice into Dutch oven; bring to a boil over medium-high heat, stirring occasionally. Boil, stirring occasionally, 15 to 17 minutes or until syrupy and a candy thermometer registers 220°. Stir in reserved 2 cups plum pulp and any accumulated juices. Stir in lime juice and cardamom. Bring to a boil over medium-high heat, stirring often. Reduce heat, and simmer, stirring constantly, 5 minutes or until very thick. Remove from heat; let foam settle (about 1 minute). Skim off and discard any foam.

Fill, seal, and process jars, leaving ¼-inch headspace and processing 5 minutes.

Remove jars from water, and let stand, undisturbed, at room temperature 24 hours. To check seals, remove the bands, and press down on the center of each lid. If the lid doesn’t move, the jar is sealed. If the lid depresses and pops up again, the jar is not sealed. Store properly sealed jars in a cool, dark place up to 1 year. Refrigerate after opening.