Put chopped rhubarb, halved cherries, and sugar in a large heavy-bottomed pot. (I used my favorite 4 qt pot, which was perfect for the task.) Add the lime juice, then stir well, cover with a clean tea towel, and let stand for 1 to 2 hours to bring the juice out of the fruit. (You can actually let this stand, covered, in the refrigerator overnight, if you need to.)
Meanwhile, prepare one more jar than you’ll think you need. The jars do not have to be sterile, but they do need to be sparkling clean. I like to take clean jars right out of the dishwasher. Wash the lids in warm sudsy water, then rinse and set aside with the bands. Put a saucer or small plate in your freezer to chill (this will be for testing doneness.) Have an extra small jar, or custard cup, clean and ready for any excess.
COOKING TIME
After the fruit macerates with the sugar and lemon juice for a while, there will be plenty of juice in the pan. Bring this to a boil over medium heat. Once the mixture boils, reduce the heat to low, then simmer the mixture until the fruit is translucent and cooked through. The smaller the pieces are, the faster this goes. When the fruit is all soft and tender, remove the pot from the heat and whiz the fruit mixture with an immersion blender to your desired texture. I like mine not quite smooth, but not lumpy. You may prefer a perfectly smooth jam.
Return the pan to the heat, and continue cooking, stirring often, until it bubbles and looks quite thick. Test for doneness by putting a spoonful on a saucer, and chilling it in the refrigerator for 2 minutes. After that time, if you can drag your finger through the jam, and leave a clear track that doesn’t fill in again, it’s ready. In my kitchen, this took about 5 minutes more.
When the jam is ready, remove the pot from the heat. Ladle jam into prepared jars, wipe rims, and apply lids and bands. Anything that won’t fit in your jars can go into the extra custard cup – don't seal it, instead cover and chill it in the fridge.
Process for 10 minutes in a boiling water bath or steam canner. Cool jars, label, and store in a dark cool place.