Aims. Our goal is to test the feasibility of obtaining accurate measurements of the continuum polarization from high-resolution spectra using the spectropolarimetric mode of ESPaDOnS. Methods. We used the new pipeline OPERA to reduce recent and archived ESPaDOnS data. Several polarization standard stars and science objects were tested for the linear mode. In addition, the circular mode was tested using several objects from the archive with expected null polarization. Synthetic broad-band polarization was computed from the ESPaDOnS continuum polarization spectra and compared with published values (when available) to quantify the accuracy of the instrument. Results. The continuum linear polarization measured by ESPaDOnS is consistent with broad-band polarimetry measurements available in the literature. The accuracy in the degree of linear polarization is around 0.2-0.3% considering the full sample. The accuracy in polarization position angle using the most polarized objects is better than 5°. Consistent with this, the instrumental polarization computed for the circular continuum polarization is also between 0.2-0.3%. Our results suggest that measurements of the continuum polarization using ESPaDOnS are viable and can be used to study many astrophysical objects.