•The heavy-ion storage ring project, the Rare-RI Ring, is ongoing at the RIKEN RI Beam Factory.•The Rare-RI Ring will enable precision isochronous mass spectrometry of r-process nuclei.•A resonant Schottky pick-up will be used for the precise tuning of isochronous optics of the storage ring.•Simulation results of 3D electromagnetic field calculations show a high sensitivity of stored single-ion detection. The new heavy-ion storage ring project Rare-RI Ring at the RIKEN RI Beam Factory launched in 2012 aims at precision isochronous mass spectrometry for single ions of exotic nuclides. To precisely tune the storage-ring ion optical conditions to the isochronous field setting, Schottky noise pick-up technique will be employed. Pillbox-type resonant cavity, similar to the Schottky pick-up system successfully operating at the experimental storage ring ESR at GSI, is adopted for the pick-up probe. To determine the design values of the cavity, we systematically performed a simulation study of three-dimensional electromagnetic field calculations in the high frequency region. High shunt impedance obtained in the simulation will enable us to detect stored single ions with charge down to q≃15.