Saving face is a way to let someone else to get out of an embarrassing or problem situation with his or her dignity intact. Sometimes people are afraid to admit that they are wrong and the negotiator can help by showing them a way out of the dilemma. This is the opposite of driving someone into a corner, which will make a person fight even harder.
Giving someone a way out is a tradition in many countries. This can work in negotiations because it is a way to avoid embarrassment and resolve the problem. Saving face is often used in politics. Something is done so that the leader does not look bad. An example was the Cuban Missile Crisis in the 1960's. Initially, neither side wanted to give in so they would not be humiliated. By helping the other side not look bad, you may be able to get some concessions.
Saving face is also a way to be creative about a solution. For example, if you have a high-ranking employee who is not doing his job, you may want to demote him or her. However, this could be devastating to the employee's ego. Perhaps, he could get a different title in the new position that does not make it so obvious that it is a demotion. In such a situation, the employee may be salvageable and not be so angry and upset about a demotion
Try finding a way not to make the other side look bad and see where it takes you. Soon you will be negotiating like a pro.