The calorimetry exchange (CALEX) program is administered by New Brunswick Laboratory (NBL). The main objective of the program is to provide an independent verification of the internal quality control practices in nuclear material safeguards facilities making plutonium accountability measurements by non-destructive calorimetry/gamma spectrometry techniques. Facilities measure the calorimetric power, and plutonium and 241Am isotope abundances of CALEX program standards using routine accountability procedures. The measurement results as well as two other quantities (effective specific power and plutonium mass) calculated from these results are evaluated for accuracy (or bias) and precision. In this paper, a limited number of measurement results of a CALEX program standard (identified as Calex I) are evaluated with specific goals to identify a suitable method for uncertainty estimation and to identify the major contributors to the uncertainties. In order to achieve the goals, the Calex I measurement results were evaluated using two different methods: the first method confined to uncertainty estimation from random variations of the measurement results alone, and the second method providing a more comprehensive evaluation of uncertainties from both the measurements and the characterized values of the measured standard according to the Guide to the Expression of Uncertainty in Measurement (GUM). The results of this study, and a subsequent study extended to a larger number of results in the CALEX program database, are expected to provide relevant input for developing the International Target Values for plutonium measurements by the calorimetry/gamma spectrometry method.