  The symmetric (Heisenberg) exchange interaction is fundamental to magnetism
and assumes critical importance in designing magnetic materials for novel
emergent phenomena and device applications. However, quantifying exchange is
extremely challenging for ultrathin ($\sim$ 1 nm) magnetic films, as techniques
and approximations reliably used for bulk materials are largely inapplicable in
the two-dimensional (2D) limit. Here we present and contrast the measurement of
exchange stiffness, $A$, by several methods on a series of five Co/Pt-based
ultrathin ($1-2$ nm) films. We compare results from (a) spin-wave spectroscopy
by Brillouin light scattering (BLS), (b) three analytical models describing the
temperature dependence of magnetization obtained by magnetometry, (c)
microscopic domain periodicity measurements and simulations, and (d) ab initio
density functional theory (DFT) calculations. While different methods present
some qualitatively consistent trends across samples, we note, for any given
sample, considerable differences (up to $5\times$) in the absolute values of
$A$ across the techniques, consistent with discrepancies of $A$ reported in
literature for nominally similar samples. We analyze possible sources of the
discrepancies across various methods, notably including their relationship to
the spin-wave dispersion, and the wave-vector ranges probed. We compare the
strengths and limitations of the techniques, and outline directions for their
future use in characterizing exchange interactions in ultrathin films.
