Several approximation techniques for the Hertz potential of an infinitesimal dipole in the presence of a conducting half space are presented. The formal solutions obtained by rigorous mathematical procedures are transformed, with the aid of some approximation, to fast convergent forms. The approximation techniques are different depending on the media where the observer and source are located. All results calculated are compared to those of the brute-force integrations of the formal solutions. Restrictions of the validity of these approximations are discussed.