At a general level, you'll want to keep doing your job as well as possible. Resist the inclination to vent about the person making the allegations - be a model of professionalism. If there is an investigation, cooperate fully and avoid being defensive. MO is an at-will employment state, so you can be fired for any (non-discriminatory) reason, or no reason at all. So avoid being an employee they want to fire.
Being wrongfully accused of harassment is awful. However, I've seen lots of people deal with it, keep their jobs and emerge from the other side with their reputations intact. You just need to avoid all of the temptations - anger at the accuser, anger at your company - that will pop up along the way and make things turn out poorly for you. Rise above!
