  Effective Field Theories (EFTs) for Goldstone Boson scattering at a low order
allow the computation of near--threshold observables in terms of a few
coefficients arranged by a counting. As a matter of principle they should make
sense up to an energy scale $E\sim 4\pi F$ but the expansion in powers of
momentum violates exact elastic unitarity and renders the derivative expansion
unreliable at much lower energies. If new--physics deviations from the Standard
Model are found and encoded in low-energy coefficients, perhaps at the LHC, it
will be profitable to extend the reach of the EFT to regimes where partial
waves are saturating unitarity. The methods known in hadron physics as
"Unitarized Chiral Perturbation Theory" extend the EFT up to its nominal reach
or up to the first new physics resonance or structure (if found below that
energy reach) in the partial wave amplitude, but they usually have unknown
uncertainties. We recapitulate our analysis of the systematic theory
uncertainties of the well known Inverse Amplitude Method (IAM).
