Smart Transformers (STs) have a key role to play in establishing hybrid ac/dc grids. This paper focuses on challenges in ensuring high-fidelity Real-Time Simulation (RTS) of switching models of STs, in particular on the RTS of a switching model of the Dual-Active Bridge (DAB) converter utilized for the dc/dc power conversion stage. Phase-shifted modulation used for the operation of DAB converters requires a relatively small simulation time-step to achieve a sufficient level of simulation fidelity. An analytical condition for the upper limit of the simulation time-step required to achieve a predefined level of simulation fidelity for a given switching frequency and operating range of the phase-shift angle of a single-phase DAB converter is introduced in this paper. However, the size of the simulation time-step must be sufficiently large to allow the calculation of the switching model of the entire power-converter system in real time, which might be in conflict with the requirement in terms of simulation fidelity. In this case, a method of oversampling the switching signals is proposed, which allows for the utilization of a simulation time-step feasible for real-time model calculation while sampling switching signals at a rate higher than the simulation time-step. Using the approaches mentioned above, the paper provides validation of the simulation fidelity of RTS of switching models of DAB converters in open-loop operation and closed-loop operation with controlled output voltage.