Comparison of 21-cm data from the Effelsberg 100-m and NRAO Greenbank 91-m telescopes are used to find the limiting precision for redshift measurement. At SNR levels of 10 or above, the random uncertainty actually achieved in a single redshift measurement is demonstrated to be 0.85 km/s at a bandwidth of 6.25 MHz. Uncertainty in other bands scales as the square root of the bandwidth relative to 6.25 MHz. Random error is also found to be independent of which telescope or software is used as long as the SNR is large. At low SNR the choice of software affects precision. Substantial systematic errors are shown to be present in some existing systems or software, due to errors in specifying the location of the center frequency. Such errors can easily be eliminated with standardized intercomparisons.