A grid resolution compensation scheme based on subgridding is proposed and evaluated for improving the performance of the finite-difference time-domain method implemented in cylindrical coordinates. The scheme introduces subgrids into the domain with smaller azimuthal grid spacings. This work investigates interpolation methods used for estimating unknown but required field values at the interface between grids with different azimuthal grid spacings. It is found that cubic, cubic spline and trigonometric interpolation cause less than 1% error in estimating the frequencies of the propagating modes of a microstructured optical fiber. Multiple subgrids have the potential for significant domain size reduction and minimum time step enlargement.