We have constructed two highly stable and reproducible (87)Rb D(2)-saturated-absorption spectrometers at 780 nm, using dither/third-harmonic lock-in detection and radio-frequency sideband techniques, respectively. We achieved +/-3-kHz reproducibility and agreement between these two independent systems. Heterodyne measurements of the hyperfine splittings of the 5P(3/2) state give its magnetic dipole (A) and electric quadrupole (B) hyperfine constants with a 10-fold reduction in uncertainty.