This paper describes the process adopted at the European Organization for Nuclear Research (CERN) to quantify uncertainties affecting the characterization of very-low-level radioactive waste. Radioactive waste is a by-product of the operation of high-energy particle accelerators. Radioactive waste must be characterized to ensure its safe disposal in final repositories. Characterizing radioactive waste means establishing the list of radionuclides together with their activities. The estimated activity levels are compared to the limits given by the national authority of the waste disposal. The quantification of the uncertainty affecting the concentration of the radionuclides is therefore essential to estimate the acceptability of the waste in the final repository but also to control the sorting, volume reduction and packaging phases of the characterization process. The characterization method consists of estimating the activity of produced radionuclides either by experimental methods or statistical approaches. The uncertainties are estimated using classical statistical methods and uncertainty propagation. A mixed multivariate random vector is built to generate random input parameters for the activity calculations. The random vector is a robust tool to account for the unknown radiological history of legacy waste. This analytical technique is also particularly useful to generate random chemical compositions of materials when the trace element concentrations are not available or cannot be measured. The methodology was validated using a waste population of legacy copper activated at CERN. The methodology introduced here represents a first approach for the uncertainty quantification (UQ) of the characterization process of waste produced at particle accelerators.