No talking while viewing a nihonto.
When you are viewing Nihonto, refrain from talking so that the Nihonto will not get your saliva. The biggest enemy of Nihonto is "moisture". They are made of iron. Even a smallest amount of water can cause rust on Nihonto. If our saliva landed on a Nihonto, it will get rusted in only several hours. Before putting a Nihonto back to "Saya", make sure to wipe off any moisture. In old days, Samurai put "Hanshi", a piece of Japanese paper, in their mouth to prevent their saliva from flying.
Be considerate of people around you.
Appreciate the beauty of nihonto.
It is very inappropriate to face the tip and the cutting part of Nihonto to other people. It is very dangerous, to begin with, but also it is a very rude action. This spirit still lives in our daily lives. The truly great Sushi chef would never put down their knives with their tips or cutting parts towards customers. Unfortunately, there may be more chefs who don't know that manner than we hope.
View Nihonto with your "internal eyes". Find a nice, quiet room where you can take time to view Nihonto. Empty your mind and relax. Depending on the condition of your mind, Nihonto might look like a fierce man or a beautiful lady in the mist. "Feeling" Nihonto is one of the joys of viewing Nihonto.