Traditional preparation methods for cytology samples pose a significant problem for Raman microspectroscopy, with long-established clinical techniques depositing cells on glass slides. Unfortunately, both the signal from the glass slide and the baseline signal from the cell itself obscure the Raman cell spectrum. The intensity of the glass signal varies from cell to cell depending on morphology, and although smooth, the signal is more complex within the fingerprint region than the baseline, and cannot be easily removed from the Raman spectrum using polynomial fitting techniques. It is difficult to accurately remove both background signals, and therefore, the use of standard glass slides compromises the capability of pre-processing methods to extract reliable and reproducible spectra from biological cells. To avoid this signal, Raman spectra are often recorded from cells on expensive substrates, such as calcium fluoride (CaF2) or quartz, but this practice is impractical for large scale applications of Raman cytology for diagnostics or screening purposes. This study investigates the potential of a number of background subtraction algorithms to remove both the glass signal and the baseline, and investigates the effect of these algorithms on subsequent multivariate analysis for the purpose of cell classification. This study demonstrates that the well-known extended multivariate signal correction (EMSC) algorithm is particularly effective in this regard, and that the results of subsequent multivariate statistical analysis are independent of the reference cell spectrum used in the algorithm. Matlab code is provided for the implementation of the EMSC algorithm