We analyze high signal-to-noise spectra for 14 globular clusters (GCs) in the Sombrero galaxy, NGC 4594 (=M104), obtained with the LRIS spectrograph on the Keck I telescope. We find generally good agreement between spectroscopic metallicities and previous photometric metallicities based on V-I colors. Further, we use measurements of various Balmer line indices on co-added spectra of metal-poor and metal-rich GCs to estimate ages for the GC subpopulations and find ages of 10-15 Gyr, with preferred ages around 11-12 Gyr and no detectable differences between the metal-rich and metal-poor subpopulations. However, because of model and measurement uncertainties, age differences of a few (2-3) gigayears cannot be ruled out. We also measure α-to-iron abundance ratios from Mg and TiO features and find enhancements on the order of [α/Fe]~+0.4, similar to the [α/Fe] abundance ratios observed in other old stellar populations. Finally, we combine our sample with radial velocities for 34 GCs from Bridges et al. and obtain virial and projected masses for the Sombrero of MVT=(8.1+/-1.8)×1011 Msolar and MP=(5.3+/-1.0)×1011 Msolar within 17 kpc, respectively. Using 12 clusters within the central 4.5 kpc the corresponding numbers are MVT=(2.1+/-1. 1)×1011 Msolar and MP=(2.0+/-1.3)×1011 Msolar. Based on data obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.