We present high signal-to-noise ratio integrated spectra of 24 star clusters in the Large Magellanic Cloud (LMC), obtained using the FLAIR spectrograph at the UK Schmidt telescope. The spectra have been placed on to the Lick/IDS system in order to test the calibration of Simple Stellar Population (SSP) models. We have compared the SSP-predicted metallicities of the clusters with those from the literature, predominantly taken from the Ca-triplet spectroscopy of Olszewski et al. (1991). We find that there is good agreement between the metallicities in the range -2.10 <=[Fe/H]<= 0. However, the Mg2 index (and to a lesser degree Mg b) systematically predict higher metallicities (up to +0.5 dex higher) than . Among the possible explanations for this are that the LMC clusters possess [α/Fe] > 0. Metallicities are presented for eleven LMC clusters which have no previous measurements. We compare SSP ages for the clusters, derived from the Hβ, Hγ and Hδ Lick/IDS indices, with the available literature data, and find good agreement for the vast majority. This includes six old globular clusters in our sample, which have ages consistent with their HST colour-magnitude diagram (CMD) ages and/or integrated colours. However, two globular clusters, NGC 1754 and NGC 2005, identified as old (~15 Gyr) on the basis of HST CMDs, have Hβ line-strengths which lead ages that are too low (~8 and ~6 Gyr respectively). These findings are inconsistent with their CMD-derived values at the 3σ level. Comparison between the horizontal branch morphology and the Balmer line strengths of these clusters suggests that the presence of blue horizontal branch stars has increased their Balmer indices by up to ~1.0 Å. We conclude that the Lick/IDS indices, used in conjunction with contemporary SSP models, are able to reproduce the ages and metallicities of the LMC clusters reassuringly well. The required extrapolations of the fitting functions and stellar libraries in the models to lower ages and low metallicities do not lead to serious systematic errors. However, owing to the significant contribution of horizontal branch stars to Balmer indices, SSP model ages derived for metal-poor globular clusters are ambiguous without a priori knowledge of horizontal branch morphology.