In recent years, nonlinear dynamic system identification using artificial neural networks has garnered attention due to its manifold potential applications in digital twins of engineering systems. However, purely data-driven approaches often struggle with extrapolation and may yield physically implausible forecasts. This makes it difficult to trust such models, especially since the learned dynamics can exhibit spurious instabilities. Physics-guided machine learning seeks to resolve these challenges by integrating physical priors and inductive biases into the model architectures. The present work proposes stable port-Hamiltonian Neural Networks (sPHNNs) as a physics-guided machine learning architecture for identifying nonlinear dynamic systems. The architecture incorporates the physical biases of energy conservation or dissipation while guaranteeing global Lyapunov stability of the learned dynamics. The approach's viability, limitations, and advantages are highlighted using illustrative examples. Further evaluation with real-world benchmark data demonstrates the sPHNN's ability to generalize from sparse data, outperforming the purely data-driven approach and avoiding instability issues. In addition, the model's potential for data-driven reduced order modeling is highlighted by training it on multi-physics simulation data to construct a surrogate model. While sPHNNs are confined to modeling globally stable systems, in their applicable domain, they promote robustness and physically plausible dynamics.