You cannot store your contacts in saliva. Nor can you clean your contacts with saliva. The salivary fluids will bring bacteria or other impurities to your contacts, thus infect your eyes. So for the health of your eyes, you should not store your contacts in saliva. If you run out of contact lenses solution, you should buy another one immediately. The contact lenses solution can moisten your contact lenses and what is more important is that it will sterile your contact lenses as well as remove the protein on the surface of the lenses. If you cannot buy a contact lenses solution, you can use sterile water to store the lenses. Homemade saline water is not recommended, for the improper portion of water and salt may damage your contact lenses as well as your eyes.
It's so disgust to keep contact lenses in saliva. There are special contact lenses solution that apply to store contact lenses. And you can get it at almost every eyeglasses shop. In fact, you can buy the solution when you buy your contact lenses. If you just happen to run out of your contact solution, you can use home-made saline to keep your contact lenses temporarily. Anyway, if you often use contact lenses, you shall prepare enough contact lenses solution all the time.
No, it is wrong to store your contacts in the saliva. There are many zymoproteins contained in the saliva which is able to decompose the materials making up your eye contact lenses, and there are also many bacteria in the saliva which will make your eyes get infected if you wear the lenses after storing them in the saliva. The right and only way to store the contact lenses when you are not wearing them is to store them in the fresh contact lens care solutions in a clean and sterilized lens container. And notice that the care solution should be changed every day in case of the bacteria multiplication.