If you are worried about someone taking or damaging your watch, you might want to opt for locked storage. It is important to keep your watches safe, especially those that have a high sentimental value, but you don't want you to just trust any watch storage to do it for you. 

If you only have one watch or prefer to store your watches individually, a watch box is a good option. A single bag really does not cost you much, and if you still have to wind it up, why not keep the watch winder? Or maybe you are just starting a collection, but you still like the idea of a bag for your watch collection. If you are unable to bring the entire watch case, you can use watch boxes. While traveling, you should use a zipped watch pocket or some other form of protection to protect your transit watch while traveling.