We describe techniques concerning wavelength calibration and sky subtraction to maximise the scientific utility of data from tunable filter instruments. While we specifically address data from the Optical System for Imaging and low Resolution Integrated Spectroscopy instrument (OSIRIS) on the 10.4~m Gran Telescopio Canarias telescope, our discussion is generalisable to data from other tunable filter instruments. A key aspect of our methodology is a coordinate transformation to polar coordinates, which simplifies matters when the tunable filter data is circularly symmetric around the optical centre. First, we present a method for rectifying inaccuracies in the wavelength calibration using OH sky emission rings. Using this technique, we improve the absolute wavelength calibration from an accuracy of 5 Angstroms to 1 Angstrom, equivalent to ~7% of our instrumental resolution, for 95% of our data. Then, we discuss a new way to estimate the background sky emission by median filtering in polar coordinates. This method suppresses contributions to the sky background from the outer envelopes of distant galaxies, maximising the fluxes of sources measured in the corresponding sky-subtracted images. We demonstrate for data tuned to a central wavelength of 7615~$\rmÅ$ that galaxy fluxes in the new sky-subtracted image are ~37% higher, versus a sky-subtracted image from existing methods for OSIRIS tunable filter data. ; Comment: MNRAS accepted; 7 pages, 6 figures