The present invention provides a method of replacing a failed pump seal of a pump having a pump housing and a rotating pump shaft. As part of the method, there is provided a specially configured rescue seal. The rescue seal is placed on the pump shaft above the failed seal so that the pump shaft extends through both the failed seal and the rescue seal. In order to affix the rescue seal to the pump shaft and above the failed seal, a plurality of studs are first attached to the pump housing after removing some of the bolts that fasten the failed seal to the pump housing. The failed seal is then secured to the studs with nuts. Nuts are then placed on the studs to secure the rescue seal to the studs above the failed seal.