Spectrophotometers are operated in numerous fields of science and industry for a variety of applications. In order to provide confidence for the measured data, analyzing the associated uncertainty is valuable. However, the uncertainty of the measurement results is often unknown or reduced to sample-related contributions. In this paper, we describe our approach for the systematic determination of the measurement uncertainty of the commercially available two-channel spectrophotometer Agilent Cary 5000 in accordance with the Guide to the expression of uncertainty in measurements. We focus on the instrumentation-related uncertainty contributions rather than the specific application and thus outline a general procedure which can be adapted for other instruments. Moreover, we discover a systematic signal deviation due to the inertia of the measurement amplifier and develop and apply a correction procedure. Thereby we increase the usable dynamic range of the instrument by more than one order of magnitude. We present methods for the quantification of the uncertainty contributions and combine them into an uncertainty budget for the device.