Quantitative measurements of electric fields at the mesoscale are essential for understanding and optimizing the performance of modern devices. However, achieving this using electron microscopy techniques is challenging due to the coexistence of electrostatic and diffraction-related contrast resulting from electron beam interactions with the material. This thesis investigates the capabilities and limitations of pixelated differential phase contrast (DPC) in scanning transmission electron microscopy for quantitatively measuring electric fields at length scales ranging from nanometers to micrometers. A progressive experimental approach is adopted, beginning with electric field measurements in vacuum to determine the sensitivity and limitations of pixelated-DPC in the absence of crystalline effects. The technique is then applied to ferroelectric perovskite BaTiO3 with an intentionally fabricated wedge-shaped sample, enabling a quantitative assessment of thickness-dependent mean inner potential contributions and polarization-induced electric fields. Precession-assisted acquisition is used to reduce the impact of diffraction contrast on the measurements. Finally, precession-assisted pixelated-DPC is combined with in situ heating and electrical biasing to correlate the evolution of 90° needle domains with local electric field measurements. The results reveal that quantitative polarization mapping under applied bias is strongly limited by additional contrast arising from specimen quality and diffraction effects. Overall, the findings of this thesis provide guidance on the experimental conditions under which pixelated-DPC can be used to reliably and quantitatively measure electric fields at the mesoscale, and maps the experimental and methodological challenges that must be overcome for its application to accurate measurements of the direction and amplitude of ferroelectric polarization.