The Maxwell system is considered in a three-dimensional domain G having several cylindrical ends. The coefficients are variable and stabilizing at infinity with exponential rate. The limit coefficients are independent of the axial coordinate in the corresponding cylinder. A scattering matrix is defined on the waveguide continuous spectrum outside of the thresholds. The matrix depends on the spectral parameter, is of finite size, which remains constant between neighbouring thresholds and changes when the parameter crosses a threshold. The scattering matrix is unitary. In the paper, we propose a method for approximate computation of the scattering matrix. Moreover, we prove the existence of finite one-side limits of this matrix at every threshold.