Physics and engineering aspects of a system for electron cyclotron resonance heating (ECRH) at the magnetic mirror device Gas Dynamic Trap (GDT, Budker Institute, Novosibirsk) are presented. This system based on two 450 kW/54.5 GHz gyrotrons is aimed at increasing the electron temperature up to the range 250-350 eV for improved energy confinement of hot ions. The basic physical issue of the GDT magnetic field topology is that conventional ECRH geometries are not accessible. The proposed solution is based on a peculiar effect of radiation trapping in inhomogeneous magnetized plasma. Under specific conditions, oblique launch of gyrotron radiation results in generation of right-hand-polarized (R) electromagnetic waves propagating with high N|| in the vicinity of the cyclotron resonance layer, which leads to effective single-pass absorption of the injected microwave power. In the present paper, we investigate numerically an optimized ECRH scenario based on the proposed mechanism of wave propagation and discuss the design of the ECRH system, which is currently under construction at the Budker Institute.