Peculiarities of ferromagnetic resonance response of conducting magnetic bi-layer films of nanometric thicknesses excited by microstrip microwave transducers have been studied theoretically. Strong asymmetry of the response has been found. Depending on the order of layers with respect to the transducer either the first higher-order standing spin wave mode, or the fundamental mode shows the largest response. Film conductivity and lowered symmetry of microwave fields of such transducers are responsible for this behavior. Amplitude of which mode is larger also depends on the driving frequency. This effect is explained as shielding of the asymmetric transducer field by eddy currents in the films. This shielding remains very efficient for films with thicknesses well below the microwave skin depth. This effect may be useful for studying buried magnetic interfaces and should be accounted for in future development of broadband inductive ferromagnetic resonance methods.