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A novel high-precision model of a custom-made coaxial chamber used for broadband measurement of the relative complex permittivity at microwave frequencies is presented. The model is based on a surface integral-equation formulation of the method of moments tailored for bodies of revolution. All singular integrals encountered in the numerical analysis are calculated in a unified way with a novel integral transformation, which enables the precision of up to 12 significant digits using the 64-bit representation of real numbers. The dielectric parameters are estimated from the reflection-coefficient measurement of the chamber with a disk-shaped dielectric sample by comparison of the measured data with the high-precision numerical analysis of the chamber. The complete measurement procedure is illustrated and verified using samples of known dielectric properties. This is the peer-reviewed version of the paper: Petrović, J.G., Olćan, D.I., Obradović, N.N., Djordjević, A.R., 2022. High-Precision Method of Moments Applied to Measurement of Dielectric Parameters at Microwave Frequencies. IEEE Transactions on Microwave Theory and Techniques, 70, 2, 970-979. [https://doi.org/10.1109/TMTT.2021.3136294]