Simulating mountain waves and associated turbulence in the upper troposphere and lower stratosphere (UTLS) remains a challenge in numerical weather prediction (NWP). We investigate how the representation of mountain‐wave dynamics and turbulence in the ICOsahedral Nonhydrostatic (ICON) model depends on model resolution and turbulence parameterization. ICON simulations were performed in NWP mode (ICON-NWP) with varying horizontal (2 km, 1 km, 500 m) and vertical (400 m, 200 m, 100 m) resolutions, using the operational turbulent kinetic energy scheme and the newly developed two-energy turbulence scheme. The simulations were evaluated against high-frequency in situ observations from the Deep Propagating Gravity Wave Experiment (DEEPWAVE) over New Zealand on 12 July 2014, as well as nested large-eddy simulations (ICON-LES) at 130 m resolution. The results show reasonable agreement with observations: ICON-LES more closely captures wavelength and phase, while ICON-NWP better reproduces wave amplitude. Near-convergence of local wave and turbulence structures requires horizontal grid spacings of 1 km or finer and vertical spacings in the UTLS of 200 m or finer. A key finding is that both turbulence schemes yield similar wave structures, despite large differences in simulated turbulent kinetic energy. This discrepancy is primarily attributed to the empirical parameterization of the horizontal shear term, which may not be realistic at very high resolutions. In terms of bulk measures, the area-averaged gravity-wave momentum flux approaches convergence already at 1 km. These results provide guidance on the resolution and turbulence representation needed for reliable simulations of small-scale mountain waves and turbulence in the UTLS.