The radiation field of relativistic charged particles moving in media with resonant dispersion is analyzed using the stationary phase method. Three medium models are considered: a model typical for dielectrics, a model typical for magnetics, and a model typical for the left-handed medium. Equations determining stationary points are obtained, and the conditions for the existence of one or two stationary points are found. A simple analytical expression for stationary points in the case of ultrarelativistic motion in resonant dielectric or magnetic materials is given. In the case of an arbitrary velocity, an algorithm for solving the stationary point equation and for computing the radiation field is developed. The results of this algorithm are compared with those obtained by computation of the field using exact formulae. Typical dependences of the field on distance from the charged particle are presented. It is shown that, for the case of the left-handed medium, the radiation field is formed at larger distances