Wavefront sensing under nonparaxial conditions was studied with Shack-Hartmann setups based on arrays of microaxicons. The robustness of the generated pseudonondiffracting subbeams against tilt and axial displacement was demonstrated for ultraflat Gaussian- and inverse-Gaussian-shaped elements in transmission and reflection. To characterize slight aberrations and to identify optimum parameter fields, spatial moments of intensity profiles were analyzed with high sensitivity. Reflective design enables for wavefront sensing at oblique incidence as necessary for low-feedback detection and phase diagnostics of ultrashort pulses.