A variant of piezo force microscopy was used to characterize the effect of strain on polarization in [(BaTiO3)n/(SrTiO3)m]p superlattices. The measurements were compared to theoretical predictions based on phase-field calculations. When polarization is constrained to be perpendicular to the substrate, the measured polarization and domain morphology agree quantitatively with the predictions. This case allows the presence of an internal electric field in the thin film to be identified. The measured trend in piezoelectric response with strain state was in qualitative agreement with predictions, and the differences were consistent with the presence of internal electrical fields. Clear differences in domain morphology with strain were observed; and in some cases, the lateral anisotropic strain appeared to influence the domain morphology. The differences in magnitude and morphology were attributed to the internal electric fields and anisotropic strains.