Experiments directed toward the realization of frequency standards of high accuracy using stored ions are briefly summarized. In one experiment, an RF oscillator is locked to a nuclear spin-flip hyperfine transition (frequency approximately 3.03×10(8) Hz) in (9 )Be(+) ions that are stored in a Penning trap and sympathetically laser-cooled. Stability is better than 3×10(-12)tau(-(1/2)) and uncertainty in Doppler shifts is estimated to be less than 5×10(-15). In a second experiment, a stable laser is used to probe an electric quadrupole transition (frequency approximately 1.07×10(15) Hz) in a single laser-cooled (199)Hg(+) ion stored in a Paul trap. The measured Q value of this transition is approximately 10(13). Future possible experiments are discussed.