The influence of electrode material, dc bias, and pellet thickness on the electrical properties of fine- and coarse-grained $\mathrm{Ca}{\mathrm{Cu}}_{3}{\mathrm{Ti}}_{4}{\mathrm{O}}_{12}$ (CCTO) ceramics has been investigated using impedance spectroscopy. The low frequency arc observed in ${\mathrm{Z}}^{*}$ plots near room temperature is independent of the electron work function of the metal electrode. It shows significant variation with dc bias and pellet thickness for coarse-grained ceramics, but no such variations for fine-grained ceramics. The results demonstrate the importance of ceramic microstructure in controlling the electrical properties of CCTO ceramics and support the internal barrier layer capacitor (IBLC) model of Schottky barriers at the grain boundaries between semiconducting grains. The IBLC model explains the high permittivity and nonlinear current-voltage characteristics commonly reported for CCTO ceramics.