  We present detailed calculations of low-energy spin dynamics in the ``ferric
wheel'' systems Na:Fe_6 and Cs:Fe_8 in a magnetic field. We compute by exact
diagonalisation the low-energy spectra and matrix elements for total-spin and
N'eel-vector components, and thus the time-dependent correlation functions of
these operators. Comparison of our results with the semiclassical theory of
coherent quantum tunnelling of the N'eel vector demonstrates the validity of a
two-state description for the low-energy dynamics of ferric wheels. We discuss
the implications of our results for mesoscopic quantum coherent phenomena, and
for the experimental techniques to observe them, in molecular magnetic rings.
