The excitation of coherent cyclotron radiation by a relativistic charged particle moving through a conducting medium has been studied. The medium consists of free electrons embedded in a host medium which has the shape of a slab of finite widthL and dielectric constant ɛh (for example, the medium could be either a semiconductor or a plasma). It is well known that, in the presence of a uniform magnetic field, which, for simplicity, is taken normal to the sides of the slab, such a medium behaves like an anisotropic uniaxial crystal. From Maxwell’s equations and boundary conditions, exact expressions, in integral form, are obtained for the electromagnetic field everywhere in space. It is shown that there are two components associated with the electromagnetic field inside the slab, namely the ordinary and the extraordinary component, as is expected from the anisotropy of the medium. It is also shown from the corresponding dispersion relations for the ordinary and extraordinary components that the index of refraction of the extraordinary component can satisfy the Cerenkov condition for frequency components close to the electron cyclotron frequency, while this condition may not be satified by the ordinary component. Therefore, the emission of Cerenkov radiation, due to the extraordinary component, is possible. By means of the method of stationary phase, approximate expressions are derived for the fields, the radiation pattern and the radiated-energy spectrum in the forward and backward directions, far away from the slab.