Vertical nesting and adaptive vertical gridding in nested mesoscale Weather Research and Forecasting (WRF)/microscale codes are developed. The inner nest of WRF is coupled with a sequence of embedded microscale nests, both horizontally and vertically. The fully three-dimensional (3D), compressible Navier-Stokes equations are solved with a stretched, adaptive grid in the vertical, with grid spacing down to a few meters in thin Clear Air Turbulence (CAT) layers where strong turbulent mixing occurs. For nesting, both lateral and vertical boundary conditions are treated via relaxation zones where the velocity and temperature fields are relaxed to those obtained from the WRF inner nest. This methodology is applied to the analysis of field data from T-REX campaign of measurements. Real case simulations based on initial and boundary conditions from high resolution T799 L91 European Centre for Medium-Range Weather Forecasts (ECMWF) analysis data are conducted. The embedded microscale nests predict localized shear layers and diagnose stiff gradients of vertical velocity and potential temperature above the tropopause and in the lower stratosphere. Three-dimensional instability mechanisms and turbulent dynamics within these CAT layers are fully resolved.