Investigations at microring electrodes are limited by the lack of equations that describe short and Ion time behavior at rings of all thicknesses. In this paper, a robust finite difference numerical method is presented for the simulation of electrochemical processes at microring electrodes of intermediate thickness. The method relies on a careful meshing strategy to minimize electrode flux errors. The accuracy of the method is first tested by comparison with a well-established reversible steady-state analytical equation. The meshes obtained through this process are reused to produce current results for chronoamperometry and linear-sweep voltammetry. In the case of chronoamperometry, simulated currents show less than 1.5% difference compared to integral-equation methods. In the case of Linear-sweep voltammetry, currents are recorded across nine decades of dimensionless scan rate. Both the dimensionless peak current and voltage at half-peak height are compared with other known methods and shown to be either comparable to or better than alternative results. In the case of the voltage at half-peak height, results are confirmed by simulations at the microdisk electrode.