Everyone knows how to clean a piece of gold or silver jewellery, usually with harsh chemicals or impregnated cleaning cloths. Because our jewellery spends such a long time exposed to the elements, it can become dull or appear dirty quite easily. This is also somewhat true of organic materials like bone, horn and ivory. Because they are natural products, they contain beautiful fluctuations in colour and surface texture. Maintaining this natural aesthetic while bringing up a lovely clean shine is actually very easy and involves no chemicals or harsh treatments.
In the case of horn and ivory, wearing it against your skin is actually maintaining its quality. If the material dries out too much it becomes brittle and deep cracks will form along the grain and split through the material. The oils from your skin will help keep it shiny and rubbing your piece regularly with your fingers is a really great thing to do. Once a month, you can treat your piece of jewellery with a light coat of natural vegetable oil like almond or olive oil. This is also a nice thing to do to horn pieces occasionally. The only problem with this treatment on scrimshaw pieces is that the oil will sometimes make the ink run from the carved design. So its best to apply with caution to the inked areas.
A lovely trick I have picked up for my scrimshaw pieces that imbues a fresh shine while not removing any of the colour is an oil-based pastel. For horn pieces that are inked in white, rub a white oil pastel over the area with the carvings, rub it in with your finger and wipe off excess with a clean soft cloth. Same goes for bone pieces with a black oil pastel. The oil in the crayon will soak into the piece while the pigment will refresh the ink! You can do this anytime your piece is looking a little dull.