  Magnetic fields play vital roles in intracluster media (ICMs), but estimating
their strengths and distributions from observations is a major challenge.
Faraday rotation measures (RMs) are widely applied to this task, so it is
critical to understand inherent uncertainties in RM analysis. In this paper, we
seek to characterize those uncertainties given the types of information
available today, independent of the specific technique used. We conduct
synthetic RM observations through the ICM of a galaxy cluster drawn from an MHD
cosmological simulation in which the magnetic field is known. We analyze the
synthetic RM observations using an analytical formalism based on commonly used
model assumptions allowing us to relate model physical variables to outcome
uncertainties. Despite the simplicity of some assumptions, and unknown physical
parameters, we are able to extract an approximate magnitude of the central
magnetic field within an apparently irreducible uncertain factor approximately
3. Principal, largely irreducible, uncertainties come from the unknown depth
along the line of sight of embedded polarized sources, the lack of robust
coherence lengths from area-constrained polarization sampling, and the unknown
scaling between ICM electron density and magnetic field strength. The
RM-estimated central magnetic field strengths span more than an order of
magnitude including the full range of synthetic experiments.
