Effective Field Theories such as HEFT, organized as momentum expansions, are a controllable approximation to strong dynamics only near threshold, as they miss exact elastic unitarity, reducing their predictive power at a higher scale if small separations from the Standard Model are found at the LHC or elsewhere. Unitarized chiral perturbation theory extends their reach to the saturation of unitarity but, generally with unknown systematics. Here I present a brief ``handbook'' on how to put to use the Inverse Amplitude Method to predict a resonance (associated with a new physics scale in Beyond the Standard Model searches) and more especially on how to control its systematic uncertainties.