  We show how complex resonance poles and threshold energies for systems in
hadron physics can be accurately obtained by using a method based on the
Pad\'{e}-approximant which was recently developed for the calculation of
resonance poles for atomic and molecular auto-ionization systems. The main
advantage of this method is the ability to calculate the resonance poles and
threshold energies from \emph{real} spectral data. In order to demonstrate the
capabilities of this method we apply it here to an analytical model as well as
to experimental data for the squared modulus of the vector pion form factor,
the S0 partial wave amplitude for $\pi\pi$ scattering and the cross section
ratio $R(s)$ for $e^+e^-$ collisions. The extracted values for the resonance
poles of the $\rho(770)$ and the $f_0(500)$ or $\sigma$ meson are in very good
agreement with the literature. When the data are noisy the prediction of decay
thresholds proves to be less accurate but feasible.
