The Astro-H (Hitomi) Soft X-ray Spectrometer (SXS) was a pioneering imaging x-ray spectrometer with 5 eV energy resolution at 6 keV. The instrument used a microcalorimeter array at the focus of a high-Throughput soft x-ray telescope to enable high-resolution nondispersive spectroscopy in the soft x-ray waveband (0.3 to 12 keV). We present the suite of ground calibration measurements acquired from 2012 to 2015, including characterization of the detector system, anti-coincidence detector, optical blocking filters, and filter-wheel filters. The calibration of the 36-pixel silicon thermistor microcalorimeter array includes parameterizations of the energy gain scale and line-spread function for each event grade over a range of instrument operating conditions, as well as quantum efficiency measurements. The x-ray transmission of the set of five Al/polyimide thin-film optical blocking filters mounted inside the SXS dewar has been modeled based on measurements at synchrotron beamlines, including with high spectral resolution at the C, N, O, and Al K-edges. In addition, we present the x-ray transmission of the dewar gate valve and of the filters mounted on the SXS filter wheel (external to the dewar), including beryllium, polyimide, and neutral density filters.