How to shine your rhodium razor after cleaning?

I cleaned up a vintage Gillette Aristocrat with isopropyl alcohol for my own peace of mind recently, the razor itself was otherwise very near mint.

Any suggestions on getting rhodium plated razors as shiny and gleaming as possible once they're sanitized and clean? 

I'm clear only the handle is rhodium plated, so is there an effective way to keep the handle and the head each brilliant and shiny?

Do you mean a Gillette US made President?  The British Aristocrats were all rhodium I believe, but then I've only had a couple in hand.  My #66 Brit appears to be all Rhodium, my Y-2 President is different and I can see a difference between the head and handle .. the earlier US Executive (undated) was/is all Rhodium I think.  In either case use the least aggressive polishing compound you can.  Flitz or Maas at the outside since the razor is near mint.  Me I'd start with a polishing cloth like the Cape Cod, rinse then dry with microfiber.

Sorry, should clarify. England-made Aristocrat, so rhodium.

Ok, that's what I suspected .. if it looks good I'd just use the microfiber.

DO NOT SOAK IN ALCOHOL! At least not very long.
I think a jewelry polishing cloth is all you need. I use one very sparingly on my Gold Aristocrat and Fat Handle Tech.