A shielding method and apparatus for an antenna disposed on an elongated support adapted for disposal within a borehole. The shield providing predetermined attenuation of one or more electromagnetic energy field components as the field components interact with the shield. The shield composed of a flexible strip or cylindrical body and respectively comprising a transverse conductive element or a transverse slot therein. The shields being adapted to cover an antenna mounted on the support. The shields being compatible for use in conjunction with saddle, tilted coils or multi-layered tri-axial coils to produce a pure transverse magnetic dipole electromagnetic field. The shields are also used in methods for shielding an antenna disposed on a support to provide predetermined attenuation of an electromagnetic field component as the field components interact with the shield.