<p>Correctly modeling the relationships between correlated, uncertain input data is crucial for producing accurate uncertainty estimates of model results. This requires both an uncertainty analysis that accounts for correlations and the appropriate communication of the results, so that other analysts can correctly interpret the reported uncertainties. However, neither is common practice in industrial ecology modeling. A typical case for correlated results is the disaggregation of a total value into uncertain shares, for which we present a practical yet robust approach to model the uncertainty. Our approach is based on two standard and two generalized Dirichlet distributions, and it uses the maximum entropy principle to choose minimally biased distribution parameters in the absence of specific known values. We discuss how correlation should be communicated to preserve accurate uncertainty information and provide examples to quantify the difference it makes to the results when the correlation is simplified or completely neglected. The proposed procedure will improve the accuracy of uncertainty quantification in Material Flow Analysis (e.g. where allocation coefficients split flows to sectors), Input Output Analysis (e.g. where aggregated environmental impact data has to be disaggregated to detailed economic sectors), and some instances in Life Cycle Assessment (e.g. where market shares are uncertain). Last but not least, to lower the technical barrier to applying these approaches, we provide easy-to-use Python and R packages which automate the approach.</p>