In this paper we present a novel general methodology which ensure a minimum uncertainty in the measurement of the real part of the permittivity of a material measured using cylindrical shielded dielectric resonators. The method is based on the fact that for any given value of the dielectric permittivity there is an optimal radius of the cylindrical dielectric rod sample. When the dielectric rod sample has the optimum radius, the width of the coverage interval associated to the real part of the dielectric permittivity measurement result --- for a given confidence level --- is reduced due to a lower sensitivity of the dielectric permittivity to be measured versus the variations in the resonant frequency. The appropriated radius of a given sample under test is calculated using Monte Carlo simulations for a specific mode and a specific resonant frequency. The results show that the confidence interval could be reduced by one order of magnitude with respect to its maximum width predicted by the uncertainty estimation performed using the Monte Carlo method (MCM) as established by the supplement 1 of the Guide to the Expression of Uncertainty in Measurement (GUM). The optimum radius of the sample under examination is fundamentally determined by the electromagnetic equations that describe the measurement and does not depend specifically of the sources of uncertainty considered.