We study the scattering of longitudinally polarized W bosons in extensions of the Standard Model where anomalous Higgs couplings to gauge sector and higher-order O(p4) operators are considered. These new couplings with respect to the Standard Model should be thought of as the low-energy remnants of some new dynamics involving the electroweak symmetry breaking sector. By imposing unitarity and causality constraints on the WW scattering amplitudes, we find relevant restrictions on the possible values of the new couplings and the presence of new dynamical resonances above 300 GeV. We investigate the properties of these new resonances and their experimental detectability. Custodial symmetry is assumed to be exact throughout, and the calculation avoids using the equivalence theorem as much as possible.