Never. The heat and detergent in dishwashers will spoil your pewter.
Wash your pewter by hand in warm water, and use a mild product only if necessary. Dry it with a soft, non-abrasive cloth. Wipe back and forth in straight lines and never rub in circles.
Cleaning Pewter with Brass Trim
It’s the same gentle treatment as for pewter only.
Only polish pewter when it needs it, which is not usually very often. Different types of finish on pewter need different treatments.
Polished pewter tends to be very smooth and shiny, and needs polished only occasionally. Buy a professional polishing cloth and it should be all you need. If your product is badly marked, you can also use a specialist metal polish which you will find locally. Always wash your pewter after polishing.
Satin Pewter has a grainy finish. It rarely needs polishing, but when it does it only needs a light buffing with some very fine steel wool (grade #0000). You should rub in straight lines only, in the direction of the grain. Never rub in circles. Only buff your product when really necessary, as it will damage the surface if it is polished too often. Never use steel wool on brass trim as this will scratch it. And always wash your pewter after polishing.
Oxidized Pewter has a dark, antique finish and should only be washed with mild soapy water and dried as above.