Prepare a boiling water bath canner and 6 half pint jars.
Peel and chop peaches.
Pit and chop cherries.
Combine fruit in a large, non-reactive pan and add sugar. Stir to combine.
Place the pan on the stove over high heat and bring to a boil. Cook, stirring regularly, until the fruit colors marry, the liquid gets thick and sticky, and the total volume in the pan reduces by a little more than 1/3.
When you like the finished consistency, remove the pan from the heat.
Funnel the preserves into the prepared jars. Wipe the rims, apply lids and rings, and process in a boiling water bath canner for 10 minutes.
When time is up, slide canner off the hot burner and remove lid. Let the jars sit in the cooling water for an additional 5 minutes (this helps prevent any siphoning that might be caused by a very rapid change in temperature).
Remove jars from canner and set them on a folded kitchen towel to cool.
When jars are cool enough to handle, test seals. Any unsealed jars should be refrigerated and used promptly. Sealed jars should be stored in a cool, dark place and used within a year or two.