Prepare canner, jars, and lids for canning.
Heat syrup ingredients over medium-high heat in a large saucpan until combined and hot. Reduce the heat to medium-low.
Heat peaches in the syrup, one layer at a time, until heated through. It should take about one minute per layer.
Use a slotted spoon to pack hot peaches (halves should be cavity-side down) into hot jars, stopping ½" below the edge of the jar.
Ladle hot syrup over the peaches, leaving ½" headspace. Remove air bubbles and add hot syrup if necessary to bring the headspace back to ½".
Wipe rims of jars, place on the lid, and screw on the band until fingertip tight.
Place jars in canner, ensuring they are covered by at least one inch of water. Bring to a boil and process pint jars for 20 minutes, or quart jars for 25 minutes.
Turn off the heat, remove canner lid, and wait 5 minutes before moving the jars to a towel on the counter to cool completely. After 24 hours, check the seal of the lids—if they don't flex when you press on the center, your peaches are safe to store at room temperature.