Measuring the spectral irradiance of solar radiation is required in many fields of science and technology. In this work, we present an in-depth discussion of the measuring procedure and required corrections for such measurements. We also describe our measurement uncertainty analysis, which is based on a Monte-Carlo procedure in accordance with the Guide to the expression of uncertainty in measurement (JCGM, Paris, 2008). For this purpose, fifteen uncertainty sources are identified, analyzed and described analytically. As a specific application example, we describe the instrumentation and procedure for determining the spectral irradiance of a solar simulator at the ISO/IEC 17 025 accredited solar cell calibration laboratory ISFH CalTeC and the corresponding measurement uncertainty analysis. Moreover, we provide a Python implementation for this calculation along with the paper. We show that for state-of-the-art instrumentation, significant uncertainty contributions arise from the reference lamp (primary calibration standard), stray light and signal-to-noise ratio. If sharp spectral features are present (which is common, e.g. for Xenon lamps), spectral bandwidth and wavelength uncertainty also contribute significantly to the overall uncertainty. © 2020 BIPM & IOP Publishing Ltd