Quarter and pit plums. Using a vegetable peeler, cut 2- to 3-inch strips of peel from orange, scraping off any white portions with a paring knife. Squeeze juice from orange; measure 1/3 cup juice.
For syrup, in a large saucepan combine the 1/3 cup orange juice, the water, sugar, port, and salt. Bring to boiling, stirring to dissolve sugar.
Pack plums, orange peel, and cinnamon sticks into hot sterilized pint canning jars, leaving a 1/2-inch headspace. Ladle hot syrup over plums, maintaining the 1/2-inch headspace. Wipe jar rims; adjust lids and screw bands.
Process filled jars in a boiling-water canner for 20 minutes (begin timing when water returns to boiling). Remove jars from canner; cool on wire racks. Makes 7 pints.