Aim. Development of the method of designing a combined electromagnetic shield, consisting of active and passive parts, to improve the effectiveness of reduction of industrial frequency magnetic field created by two-circuit overhead power lines in residential buildings. Methodology. The problem of design of combined electromagnetic shield including robust system of active shielding and electromagnetic passive shield of initial magnetic field solved based on of the multi-criteria two-player antagonistic game. The game payoff vector calculated based on the finite element calculations system COMSOL Muliphysics. The game solution calculated based on the particles multiswarm optimization algorithms. During the design of combined electromagnetic shields spatial location coordinates of shielding winding, the currents and phases in the shielding winding of active shielding, geometric dimensions and thickness of the electromagnetic passive shield are calculated. Results. The results of theoretical and experimental studies of combined electromagnetic passive and active shielding of magnetic field in residential building from power transmission line with a «Barrel» type arrangement of wires presented. Originality. For the first time the method of designing a combined electromagnetic shield, consisting of active and passive parts, for more effective reduction of the magnetic field of industrial frequency created by two-circuit overhead power lines in residential buildings is developed. Practical value. Based on results of calculated and experimental study the shielding efficiency of the initial magnetic field determined that shielding factors whith only electromagnetic passive shield is more 2 units, whith only active shield is more 4 units and with combined electromagnetic passive and active shield is more 10 units. It is shown the possibility to reduce the level of magnetic field induction in residential building from power transmission line with a «Barrel» type arrangement of wires by means of a combined electromagnetic passive and active shielding with single compensating winding to 0.5 μT level safe for the population. References 53, figures 15.