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In future power systems, the detailed structure and dynamics may not always be fully known. This is due to an increasing number of distributed energy resources, such as photovoltaic generators, battery storage systems, heat pumps and electric vehicles, as well as a shift towards active distribution grids. Obtaining physically-based models for simulation and control synthesis can therefore become challenging. Differential equations, where the right-hand side is represented by a neural network, i.e., neural ordinary differential equations (NODEs), have a great potential to serve as a data-driven black-box model to overcome this challenge. This paper explores their use in identifying the dynamics of droop-controlled grid-forming units based on inputs and state measurements. In numerical studies, various NODE structures used with different numerical solvers are trained and evaluated. Moreover, they are compared to the sparse identification of nonlinear dynamics (SINDy) method. The results demonstrate that even though SINDy yields more accurate models, NODEs achieve good prediction performance without prior knowledge about the system's nonlinearities which SINDy requires to work best.