This dataset contains Monte Carlo simulation results supporting the figures presented in the article "Trapping potentials and quantum gates for microwave-dressed Rydberg atoms on an atom chip" (arXiv:2504.10349). The data correspond to simulations of two microwave-dressed Rydberg atoms trapped near a surface producing a non-homogeneous electric field, representing two qubits interacting via a microwave resonator. These simulations were used to verify and characterize the performance of optimized high-fidelity quantum gate operations between the two atoms, taking into account the spontaneous decay of the Rydberg states and the decoherence induced by thermal photons in the microwave resonator. The provided CSV files include the data for: Figure 3b: Optimal detuning and SWAP time versus the thermal photon number. Figure 3c: Population of states |01⟩ and |10⟩ versus time. Figure 3d: Population of the target state |10⟩ and sum of atomic state populations at SWAP time versus the thermal photon number. Figure 4: Optimized resonator-mediated √SWAP gate fidelity versus the thermal photon number. Simulation parameters, methods, and physical assumptions are described in detail in the associated article.