We study the localisation and the existence of the eigenvalues of the generator of a contraction semigroup related to dissipative boundary problems for Maxwell system. The spectrum of the generator in the left half plane is formed by isolated eigenvalues with finite multiplicities and the corresponding solutions have an exponentially decreasing global energy. The localisation of such eigenvalues is important for the inverse scattering problems. We show that the eigenvalues are localisated in parabolic neighborhoods of the real axis or the imaginary one. For the ball we prove more precise results and we establish the existence of an infinite number of negative real eigenvalues.