We numerically investigate crystalline order on negative Gaussian curvature capillary bridges. In agreement with the experimental results in [W. Irvine et al., Nature, Pleats in crystals on curved surfaces, 2010, 468, 947] we observe for decreasing integrated Gaussian curvature, a sequence of transitions, from no defects to isolated dislocations, pleats, scars and isolated sevenfold disclinations. We especially focus on the dependency of topological charge on the integrated Gaussian curvature, for which we observe, again in agreement with the experimental results, no net disclination for an integrated curvature down to −10, and an approximately linear behavior from there on until the disclinations match the integrated curvature of −12. In contrast to previous studies in which ground states for each geometry are searched for, we here show that the experimental results, which are likely to be in a metastable state, can be best resembled by mimicking the experimental settings and continuously changing the geometry. The obtained configurations are only low energy local minima. The results are computed using a phase field crystal approach on catenoid-like surfaces and are highly sensitive to the initialization.