  In this work, the uncertainties in the dielectric constants of polar liquids,
computed using molecular dynamics (MD) simulations, are compared for two
different calculations schemes. Expressions of the uncertainty are derived for
the external field method, and compared with those of the fluctuation method.
Significant differences on their the system size dependence were found. In
addition, alternative calculation procedures are proposed. The individual
contributions of different parts of the system to the electric susceptibility,
and their corresponding uncertainties, are also studied. Additionally, the
effects of the sampling frequency on the uncertainties are analyzed. MD
simulations of pure liquid water (SPC/E) at 298.15 K and 1 bar were performed
in order to corroborate the obtained results. In such conditions, the best
estimate of the dielectric constant obtained in this study is 70.46$\pm$0.31.
