We constructed a quasi-analytical self-consistent model of the stripline-based broadband ferromagnetic resonance (FMR) measurements of ferromagnetic films. Exchange-free description of magnetization dynamics in the films allowed us to obtain simple analytical expressions. They enable quick and efficient numerical simulations of the dynamics. With this model we studied the contribution of radiation losses to the ferromagnetic resonance linewidth, as measured with the stripline FMR. We found that for films with large conductivity of metals the radiation losses are significantly smaller than for magneto-insulating films. Excitation of microwave eddy currents in these materials contributes to the total microwave impedance of the system. This leads to impedance mismatch with the film environment resulting in decoupling of the film from the environment and, ultimately, to smaller radiation losses. We also show that the radiation losses drop with an increase in the stripline width and when the sample is lifted up from the stripline surface. Hence, in order to eliminate this measurement artifact one needs to use wide striplines and introduce a spacer between the film and the sample surface. The radiation losses contribution is larger for thicker films.