A critical early phase for any synchrotron beamline involves detailed testing, characterization and commissioning; this is especially true of a beamline as ambitious and complex as the Imaging & Medical Beamline (IMBL) at the Australian Synchrotron. IMBL staff and expert users have been performing precise experiments aimed at quantitative characterization of the primary polychromatic and monochromatic X-ray beams, with particular emphasis placed on the wiggler insertion devices (IDs), the primary-slit system and any in vacuo and ex vacuo filters. The findings from these studies will be described herein. These results will benefit IMBL and other users in the future, especially those for whom detailed knowledge of the X-ray beam spectrum (or `quality') and flux density is important. This information is critical for radiotherapy and radiobiology users, who ultimately need to know (to better than 5%) what X-ray dose or dose rate is being delivered to their samples. Various correction factors associated with ionization-chamber (IC) dosimetry have been accounted for, e.g. ion recombination, electron-loss effects. A new and innovative approach has been developed in this regard, which can provide confirmation of key parameter values such as the magnetic field in the wiggler and the effective thickness of key filters. IMBL commenced operation in December 2008 with an Advanced Photon Source (APS) wiggler as the (interim) ID. A superconducting multi-pole wiggler was installed and operational in January 2013. Results are obtained for both of these IDs and useful comparisons are made. A comprehensive model of the IMBL has been developed, embodied in a new computer program named spec.exe, which has been validated against a variety of experimental measurements. Having demonstrated the reliability and robustness of the model, it is then possible to use it in a practical and predictive manner. It is hoped that spec.exe will prove to be a useful resource for synchrotron science in general, and for hard X-ray beamlines, whether they are based on bending magnets or insertion devices, in particular. In due course, it is planned to make spec.exe freely available to other synchrotron scientists.