Do not accept the silent treatment from your partner. Silence does not fix anything. If anything, silence in a relationship does far more harm than good.
Give your partner fair warning that the silent treatment is not going to work. If your partner will not speak to you, make it clear that this behavior is unacceptable. Emphasize that you are willing to talk about the problem, but if your partner will not speak to you, you will assume that everything is all right and that your partner is simply being rude.
Respect yourself, and do not grovel, plead or beg for your partner to stop the silent treatment. If you allow yourself to be affected by the silent treatment, your partner will think that giving the cold shoulder works, and will use it in the future.
Do not allow the silent treatment to continue. Your partner needs to understand that you will not tolerate being ignored, and that maintaining the silence will lead to the end of the relationship.
Be the better person, and do not use the silent treatment on others. Not talking about problems in a relationship only allows negative feelings to fester. Problems do not get solved through silence. While talking about things might not solve the problem immediately, at least it starts the healing process.