The cause of sickle-cell anemia to be a molecular defect was discovered in 1949 by Linus Pauling. In his experiment hemoglobin molecules were broken down to smaller fragments, which were then subjected to electrophoresis and chromatography. The results of these measurements were compared between healthy and affected samples, allowing the identification of a mutated fragment. The amino acids in the mutated fragment were analyzed in 1956 by Vernon Ingram, identifying the single mutation. The process in a bit more detail is described on this webpage.
Site-directed mutagenesis is used primarily in research aimed at finding a gene therapy based treatment for sickle-cell disease, such an attempt is described in this publication.
Also, the technique was used on recombinant hemoglobin to create and study some properties of naturally not occurring mutations. [[Link]](