Vector boson scattering (VBS) plays a central role in the search for new physics at collider experiments such as ATLAS and CMS at the LHC. Usually predictions for this kind of processes are obtained using perturbative approaches in fixed gauges. Here we present a fully gauge-invariant study of VBS in the scalar-channel involving a SM-like Higgs with finite extent. To this end, we combine results obtained in a reduced SM setup from (augmented) perturbation theory with those from non-perturbative lattice simulations.