Piezoelectric metasurfaces have been investigated as means of introducing remarkable methods of vibration mitigation and control; including energy harvesting, mode localization, vibration absorption, and elastic waveguiding. The full-scale realization of such devices remains a considerable challenge, however, due to the high precision required in the synthesis and calibration of the electrical shunts in the presence of parametric and practical uncertainties. This paper establishes a systematic methodology for assessing the susceptibility of resonant piezoelectric waveguides to variations in local properties. An analytical procedure based on the transfer matrix approach and phase gradient design is applied to calibrate the metasurface for anomalous elastic-wave refraction at a specified target angle. Numerical simulations demonstrate good agreement with the initial design, and subsequently enable local LC-resonances, parasitic resistances, and piezoelectric coupling to be individually perturbed. An experimentally based uncertainty quantification is applied to determine reasonable bounds of uncertainty in these parameters, which is applied to a Sobol sensitivity analysis leveraging the finite element model. This approach is used to rank and compare the cumulative impact of spatially distributed uncertainty on the realized refraction angle. The findings identify local resonance and piezoelectric coupling as the most influential parameters, facilitating a practical understanding of piezoelectric waveguide performance while forming the basis for subsequent advancement in uncertainty assessment and testbed implementation.