We present a simulation method for light emitted in uniaxially anisotropic light-emitting thin film devices. The simulation is based on the radiation of dipole antennas inside a one-dimensional microcavity. Any layer in the microcaviy can be uniaxially anisotropic with an arbitrary orientation of the optical axis. A plane wave expansion for the field of an elementary dipole inside an anisotropic medium is derived from Maxwell's equations. We employ the scattering matrix method to calculate the emission by dipoles inside an anisotropic microcavity. The simulation method is applied to calculate the emission of dipole antennas in a number of cases: a dipole antenna in an infinite medium, emission into anisotropic slab waveguides and waveguides in liquid crystals. The dependency of the intensity and the polarization on the direction of emission is illustrated for a number of anisotropic microcavities.