In the context of nuclear disarmament, robust verification mechanisms to assess the completeness of fissile material baseline declarations are lacking. In the field of nuclear archaeology, the Isotope Ratio Method (IRM) has been proposed as a way to use measurements of materials in the long-lasting structures of shut-down reactors to infer the quantities of produced plutonium. We propose a method of assessing the systematic uncertainties associated with IRM, focusing on incomplete information relating to the reactor operation as well as uncertainties in nuclear cross-section data. We develop a model to reconstruct plutonium production from a measurement of either B-10/B-11 of Ti-48/Ti-49 given a set of input parameters regarding the assumed operation. The application of this reconstruction model is studied for two different reactor types: a CANDU pressurized heavy water reactor and the graphite moderated reactor at Yongbyon in North Korea. With several estimates for input parameter uncertainties, we use quasi-Monte Carlo methods to estimate the output uncertainty of the model. Single value estimates of the plutonium production in our considered scenarios have an uncertainty of 4 to 11 %. So, depending on the prior knowledge on the operational history of the considered reactor, the uncertainty can be significantly larger than previous studies have suggested.