I will discuss a few non-perturbative techniques, inherited from QCD, that may be useful to characterise new strongly-coupled physics at the multi-TeV scale. Specifically, I will consider a gauge theory of fermions, that confines and realizes the Higgs particle as a composite Goldstone boson. The focus will be to determine the spectrum of meson resonances that accompany the Higgs. To this end, we approximated the hypercolour dynamics by four-fermion operators, à la Nambu-Jona Lasinio, as motivated by large-N arguments. Models with both a Goldstone Higgs and top-quark partners actually require a two-sector gauge theory. In this case, we found that the anomaly structure of the theory is qualitatively different from the QCD-like case. I will identify the conditions for the various meson resonances to lie within the reach of the LHC.