An on-body antenna is provided that overcomes mismatch loss problems associated with current on-body antennas and is capable of operating over a wide range of frequencies with low transmission loss. At least a first antenna element of the on-body antenna is configured to receive an oscillating electric current and to radiate an oscillating electromagnetic field over a predetermined range of frequencies. The first antenna element is made of non-electrically-conductive material having a first relative permittivity. At least a second material having a second relative permittivity can be disposed on or in the first antenna element. Disposing the second material provides the first antenna element with an effective permittivity that can be closely matched to a frequency-dependent permittivity of biological tissue of a subject. The first non-electrically-conductive material and the second material can be preselected to have relative permittivities that allow anisotropy to be achieved.