This dataset includes the code and numerical data to reproduce the results from the paper titled "Symplecticity-preserving prediction of parameter-dependent Hamiltonian dynamics by generalized kernel interpolation" (2026). The data were generated by the provided Python scripts from Hamiltonian test systems and are organized according to the corresponding numerical experiments. They include training data, computed trajectories, reference solutions, fitted surrogate models, and error quantities. The dataset can be used to rerun the experiments, reproduce the figures, and further test structure-preserving kernel surrogate methods. See the README for more information and installation instructions.