We study the use of the standard Higgs boson, with {ital m}{sub {ital H}}{gt}700 GeV, as a model for a resonance in longitudinal-vector-boson scattering. We focus on the constraint placed upon the modulus of the amplitude by unitarity. We show that it is better to use the energy-dependent width {Gamma}({ital s})={Gamma}{sub {ital H}}{times}({ital s}/{ital m}{sub {ital H}}{sup 2}){sup 2} in the Higgs-boson propagator, rather than the usual approximation {Gamma}({ital s})={Gamma}{sub {ital H}}. The {ital s}-channel approximation, the effective-{ital W} approximation, and the full electroweak {ital qq}{r arrow}{ital qqVV} process are discussed.