We have employed the method of shelving to measure Zeeman resonances of a single trapped Ba+ ion. We use optical pumping to place the ion in a selected magnetic sublevel of either the 6S1/2 ground state or the 5D3/2 metastable state. The ion is exposed to an rf field, and a probing/shelving mechanism detects whether spin-flip transitions have taken place. We have observed rf transitions with linewidths of 15 Hz, limited by magnetic-field noise. We have also observed the shift in the Zeeman frequency when the ion is illuminated by off-resonant light. A simultaneous measurement of such light shifts in two atomic states of Ba+ will permit a precise determination of the ratio of transition matrix elements.