Generally speaking, it would be most appropriate to use the Notwithstanding Clause in situations where national security is at risk, or in situations where allowing certain rights would endanger the public. Because of its controversial nature, it has never been used by the Canadian Federal Government. However, some of the provinces have used it for various reasons.
For example, while Quebec did not sign the Charter, it did pass a form of the notwithstanding clause to its own books. This was used in a famous case where signs were ordered to be posted only in French; the notwithstanding clause was invoked to temporarily suspend Freedom of Expression and Freedom of Equality, thus preventing citizens and businesses from posting signs in other languages. In this case, Quebec considered the provincial language of French to be vital to the national identity, and so considered it acceptable to withhold those rights to keep French public as the public norm.