Accurate and computationally efficient surrogate and reduced-order models are a key enabler for the data-driven analysis, design, and optimization of complex engineering systems. While purely data-driven machine learning models are efficient, they often suffer from limited robustness, poor extrapolation, and a lack of physical interpretability, particularly in small-data regimes. Scientific machine learning addresses these limitations by integrating mathematical structure and physical principles directly into learning architectures. This contribution presents stable port-Hamiltonian Neural Networks (sPHNNs) as a physics-aware machine learning framework for nonlinear dynamic system identification and surrogate modeling. The approach combines the port-Hamiltonian formalism from dynamical systems theory with neural network approximation to learn low-dimensional nonlinear state-space models from data. Conservative and dissipative dynamics are represented explicitly through a learned Hamiltonian energy function and structurally constrained interconnection and dissipation operators. By enforcing an energy balance relation and convexity constraints on the Hamiltonian, the model guarantees Lyapunov stability and bounded trajectories by construction and ensures global asymptotic stability in strictly dissipative settings. From a computational and mathematical perspective, sPHNNs embed stability and thermodynamic consistency as hard constraints within a flexible learning architecture. These guarantees enable robust generalization from sparse or noisy data and prevent non-physical behavior. Numerical experiments on real-world benchmark datasets demonstrate improved accuracy and stability compared to purely data-driven alternatives. 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. When utilizing augmented dimensions, the stability constraint enables a safe and stable exploration of the added flexibility. While sPHNNs are confined to modeling globally stable systems, in their applicable domain, they promote robustness and physically plausible dynamics.