We discuss details of the spectral fitting procedures and algorithms used in deriving line count rates for the calibration of AXAF (the Advanced X-ray Astrophysics Facility) during end-to-end testing in the winter and spring of 1996/1997. An approach involving simultaneously fitting both detector and source parameters was implemented within XSPEC, a standard x-ray spectral fitting package (Arnaud 1996). Theoretical and practical difficulties in fitting spectra taken with flow proportional counters (FPC) and solid state detectors (SSD) are discussed, including both effects incorporated into the numerical model, and those which must be estimated outside the model. Sensitivity of the parameter of interest, the counts in a strong line in the spectrum, to changes and errors in the other fit parameters is explored. The impact of uncertainties on the overall absolute AXAF calibration is discussed.