On the basis of a recently developed nonlinear guiding center theory for the perpendicular spatial diffusion coefficient $kappa$$perp$ used to describe the transport of energetic particles, we construct a model for diffusive particle acceleration at highly perpendicular shocks, i.e., shocks whose upstream magnetic field is almost orthogonal to the shock normal. We use $kappa$$perp$ to investigate energetic particle anisotropy and injection energy at shocks of all obliquities, finding that at 1 AU, for example, parallel and perpendicular shocks can inject protons with equal facility. It is only at highly perpendicular shocks that very high injection energies are necessary. Similar results hold for the termination shock. Furthermore, the inclusion of self-consistent wave excitation at quasiparallel shocks in evaluating the particle acceleration timescale ensures that it is significantly smaller than that for highly perpendicular shocks at low to intermediate energies and comparable at high energies. Thus higher proton energies are achieved at quasiparallel rather than highly perpendicular interplanetary shocks within 1 AU. However, both injection energy and the acceleration timescale at highly perpendicular shocks are sensitive to assumptions about the ratio of the two-dimensional (2-D) correlation length scale to the slab correlation length scale λ2D/λ$parallel$. Model proton spectra and intensity profiles accelerated by a highly perpendicular interplanetary shock are compared to an identical but parallel interplanetary shock, revealing important distinctions. Finally, we present observations of highly perpendicular interplanetary shocks that show that the absence of upstream wave activity does not inhibit particle acceleration at a perpendicular shock. The accelerated particle distributions closely resemble those expected of diffusive shock acceleration, and observed at oblique shocks, an example of which is shown.