The James Webb Space Telescope (JWST) mission is a collaborative project between the National Aeronautics and Space Administration (NASA), the European Space Agency (ESA) and the Canadian Space Agency (CSA). JWST is considered the successor to the Hubble Space Telescope (HST) and although its design and science objectives are quite different, JWST is expected to yield equivalently astonishing breakthroughs in infrared space science. Due to be launched in 2013 from the French Guiana, the JWST observatory will be placed in an orbit around the anti- Sun Earth-Sun Lagrangian point, L2, by an Ariane 5 launcher provided by ESA. The payload on board the JWST observatory consists of four main scientific instruments: a near-infrared camera (NIRCam), a mid-infrared camera/spectrograph (MIRI), a near-infrared tunable filter (TFI) and a near-infrared spectrograph (NIRSpec). The instrument suite is completed by a Fine Guidance Sensor (FGS). NIRSpec is a multi-object spectrograph capable of measuring the spectra of about 100 objects simultaneously at low (R~100), medium (R~1000) and high (R~2700) resolutions over the wavelength range between 0.6 micron and 5.0 micron. It features also a classical fix-slits spectroscopy mode as well as a 3D-spectrography mode with spectral resolutions up to 2700. The availability of extensive and accurate calibration data of the NIRSpec instrument is a key element to ensure that the nominal performance of the instrument will be achieved and that high-quality processed data will be made available to the users. In this context, an on-ground calibration is planned at instrument level that will supplement the later in-flight calibration campaign. In this article we describe the overall on-ground instrument calibration campaigns and we provide an overview of the main features and performances of the individual elements of the sophisticated cryogenic optical ground support equipment (OGSE) used to calibrate NIRSpec.