Radar altimeters are essential tools for observing the cryosphere, especially for estimating ice-sheet elevation change and sea-ice thickness. However, retrieving these quantities remains challenging, and progress depends on physically based numerical simulations of the recorded waveforms to understand their sensitivity to the geophysical parameters of the medium. Such models can also guide the design of future satellite missions. Accurate simulations require a balanced combination of a realistic description of the medium, precise calculation of wave–medium interactions, and an accurate representation of the altimeter measurement process, including downstream processing. The Snow Microwave Radiative Transfer (SMRT) model has addressed the first two aspects for a decade and includes an altimetric Low Resolution Mode (LRM) module, but has, until now, lacked a delay-Doppler (SAR) altimetric capability used by most modern sensors. This study introduces the new SMRT SAR altimetry module, which operates in three steps. First, it calculates the backscatter of all layers and interfaces using existing SMRT modules. Next, it models the waveforms of each layer and interface using a delay-Doppler approach. Finally, these components are combined to produce the final waveform. The user selects the delay-Doppler model from one of eight formulations reviewed, implemented, and compared in the literature. The validation first assesses these models under simple conditions, confirming they produce consistent results but differ in computational efficiency and flexibility. Subsequently, the new module is compared with external models to confirm its accuracy. Finally, it is applied to Antarctic conditions, where the simulations reproduce observed Sentinel-3 waveform variability linked to surface roughness. The open-source module, equipped with the eight options, now enables a wide range of numerical experiments, from studying penetration bias to exploring the potential for snow retrieval on sea ice and lake ice thickness.