Wash the jars and keep them warm, and fill the water bath canner and set it over heat so it comes up to a boil while you make the jam. Have lids, rings, and a funnel laid out and ready.
Rinse the plums and sort out any that are soft or split. Halve each one with a paring knife and push the stone out with your thumb. Leave the skins on.
Add the pitted plums, sugar, lemon juice, and water to a wide, heavy-bottomed pot all at once. There's no need to macerate the fruit first.
Bring the pot to a boil over high heat, stirring constantly and pressing the plum halves against the side of the pot as they soften so they break down and the sugar dissolves.
Keep the jam at a hard rolling boil, stirring the whole time, until it reaches the gel stage at 220 degrees F on an instant-read thermometer. Expect about 15 to 20 minutes once the jam has come to a full boil, but stoves vary, so go by temperature. If you'd rather not use a thermometer, drop a spoonful onto a frozen plate, return it to the freezer for a minute, and push the edge with a fingertip. If it wrinkles and holds its shape, it's done.
Ladle the hot jam into the prepared jars, leaving 1/4 inch headspace. Slide a bubble tool around the inside of each jar to release trapped air, wipe the rims clean, center the lids, and apply the rings to fingertip tight.
Lower the jars into the boiling water bath canner, making sure they're covered by at least 1 inch of water, and process for 10 minutes, adjusting for altitude (see notes). Turn off the heat and let the jars stand in the canner for 5 minutes before removing them.
Cool the jars undisturbed on a towel-lined counter for 12 to 24 hours, then remove the rings and check the seals before labeling and storing.