Determining symmetric (Heisenberg) exchange in an ultrathin magnetic film is challenging because all known experimental methods require knowledge of several other material parameters. We present and compare results of different methods based on the probing of spin waves to determine the symmetric exchange in a series of Co/Pt-based ultrathin magnetic films, hosting varying extents of chirality. The first is Brillouin light scattering spectroscopy which allows us to study the spin-wave spectrum near the Brillouin zone origin. In addition, systematic measurements of the saturation magnetization as a function of temperature MS(T ) are utilized, which effectively probe the population of the spin-wave spectrum over a significant part of the Brillouin zone. Here, different models are applied and discussed in the view of the thin film character of the samples and an analysis of the spin-wave density of states is employed to evaluate limitations of theoretical MS(T ) models. We compare the experimental results to ab initio density functional theory calculations. Although qualitative trends are apparent, we note significant differences in the absolute values of the exchange constants obtained by the various methods. Our results elucidate the origin of the large scatter in exchange constants reported in the literature for nominally very similar thin film systems. We find and explain that MS(T )-based methods tend to give lower values for the symmetric exchange compared to an analysis of the dispersion relation close to the Brillouin zone origin. Given the importance of the symmetric exchange for applications of magnetic thin films, we hope our findings proof useful when it comes to the characterization of other thin film systems.