  The scalar septet model extends the Standard Model Higgs sector by an isospin
septet with hypercharge chosen to preserve $\rho \equiv M_W^2/M_Z^2
\cos^2\theta_W = 1$. In this paper we constrain the model at high septet masses
using perturbative unitarity of longitudinal vector boson scattering
amplitudes. We also apply the constraints from LHC searches for doubly-charged
Higgs bosons produced in vector boson fusion, which constrain the model at
lower septet masses. We point out some important differences between the septet
model and extended Higgs models that preserve custodial symmetry in the scalar
spectrum.
