  We assess the principal statistical and physical uncertainties associated
with the determination of magnetic field strengths in clusters of galaxies from
measurements of Faraday rotation (FR) and Compton-synchrotron emissions. In the
former case a basic limitation is noted, that the relative uncertainty in the
estimation of the mean-squared FR will generally be at least one third. Even
greater uncertainty stems from the crucial dependence of the Faraday-deduced
field on the coherence length scale characterizing its random orientation; we
further elaborate this dependence, and argue that previous estimates of the
field are likely to be too high by a factor of a few. Lack of detailed spatial
information on the radio emission--and the recently deduced nonthermal X-ray
emission in four clusters--has led to an underestimation of the mean value of
the field in cluster cores. We conclude therefore that it is premature to draw
definite quantitative conclusions from the previously-claimed
seemingly-discrepant values of the field determined by these two methods.
