We investigate the utility of the tunable filters (TFs) for obtaining flux-calibrated emission-line maps of extended objects such as galactic nebulae and nearby galaxies using the Optical System for Imaging and low Resolution Integrated Spectroscopy (OSIRIS) at the 10.4-m Gran Telescopio Canarias (GTC). Despite the relatively large field of view (FoV) of OSIRIS (8' × 8'), the change in wavelength across the field (˜80 Å) and the long tail of the TF spectral response function are hindrances for obtaining accurate flux-calibrated emission-line maps of extended sources. The purpose of this article is to demonstrate that emission-line maps useful for diagnostics of nebulae can be generated over the entire FoV of OSIRIS if we make use of theoretically well-understood characteristics of TFs. We have successfully generated the flux-calibrated images of the nearby large late-type spiral galaxy M101 in the emission lines of Hα, [N II]λ6583, [S II]λ6716 and [S II]λ6731. We find that the present uncertainty in setting the central wavelength of TFs (˜1 Å) is the biggest source of error in the emission-line fluxes. By comparing the Hα fluxes of H II regions in our images with the fluxes derived from Hα images obtained using narrow-band filters, we estimate an error of ˜11% in our fluxes. The flux-calibration of the images was carried out by fitting the Sloan Digital Sky Survey (SDSS) griz magnitudes of in-frame stars with the stellar spectra from the SDSS spectral database. This method resulted in an accuracy of 3% in flux-calibration of any narrow-band image, which is as good as, if not better than, what has been feasible using the observations of spectrophotometric standard stars. Thus time-consuming calibration images need not be taken. A user-friendly script under the IRAF environment was developed and is available on request.