There are two schools of thought when it comes to cleaning or polishing American Indian silver. The first school of thought is that it was shiny when it was made, and it should be shiny now. The second is that patina is part of the history of any object, and should be left alone as much as possible. Both sides have their points, and both have their problems. So, which is it? Do we scrub all our silver down with a Brillo pad until it gleams like a mirror in the noonday sun? Or do we let it turn black with tarnish? In our minds, the answer is neither, and depends on the piece.
In general, tarnish on silver is a bad thing. Generations of English butlers can't be all wrong--the family silver needs to be polished. But does this hold true for antique Navajo silver? Should we bring out our silver polishing cream and make it gleam? Not really, no. We only used silver polishing cream when a piece has tarnished so badly that it is completely black, and the stamped or filed designs can no longer be seen. It is far preferable to use nothing but a silver polishing cloth to get off as much of the tarnish as will come, which is usually most of it. A general rule of thumb is that for unsigned pieces from before 1940, a polishing cloth is the only thing you should be using.
But what about more contemporary pieces done by known artists like Frank Patania Sr.? There, things are different. Unlike older pieces, the bright shine of the unstamped silver is an integral part of the beauty of the piece. This box is an excellent example:
The silver, unsullied by any markings, is supposed to stand alone and accent the turquoise setting in the center. In this case, it would be a crime to leave any tarnish on the smooth surface, which may mean using polishing cream.
In sum, if the artist used a smooth expanse of silver as a decorative element, we owe it to him /her to keep that surface as clean as possible. Therefore, polish away.