We propose a new ring ion-trapping system, that is advantageous for use in frequency-standard applications and ultrahigh-resolution spectroscopy. The ring trap can store a large number of ions with low susceptibility to the second-order Doppler effect. The ring-trap electrodes also form a wide-band microwave cavity. Microwave radiation trapping during the probe cycle makes it possible to meet the Lamb-Dicke criterion more satisfactorily than with an rf/dc hybrid linear trap, in which traveling microwave power is used. This technique yields an increased S/N ratio because the microwave probing power is absorbed in the fundamental mode rather than in the sidebands induced by ion motion in the trap. This paper presents an analytical model of the ring-trap system and estimates of the main parameters of the ring trap.