The Higgs sector in neutral naturalness models provides a portal to the hidden sectors, and thus measurements of Higgs couplings at current and future colliders play a central role in constraining the parameter space of the model. We investigate a class of neutral naturalness models, in which the Higgs boson is a pseudo-Goldstone boson from the universal SO(N)/SO(N-1) coset structure. Integrating out the radial mode from the spontaneous global symmetry breaking, we obtain various dimension-six operators in the Standard Model effective field theory, and calculate the low energy Higgs effective potential with radiative corrections included. We perform a chi-square fit to the Higgs coupling precision measurements at current and future colliders and show that the new physics scale could be explored up to 2.7 (2.8) TeV without (with) the Higgs invisible decay channels at future Higgs factories.