Shroud cavities in aero engines are typically formed by a labyrinth seal between the rotating turbine shroud and the stationary casing wall. To mitigate rub-in and reduce weight, the casing often features honeycomb structures above the rotor seal fins. In this paper, the aerodynamic performance of such honeycomb structures is experimentally investigated using a rotating test rig featuring both smooth and honeycomb-tapered casing walls. Measurements show that the discharge coefficient decreases for the honeycomb configuration while losses and subsequent windage heating of the flow increase. A variation in rotational speed reveals additional sensitivities to the local flow field in the swirl chamber. Numerical simulations are conducted and validated using the experiments. A good agreement between the prediction and measurements of the jet via the evolution of pressure across the sealing fins is identified. In contrast, the prediction of losses and integral parameters reveals larger deficits. Empirical correlations from available literature satisfactorily predict the leakage mass flow rate if rotation is low and if the casing is smooth. High rotation and the presence of honeycombs, however, prove challenging and reveal the potential for further improvements. We propose a simple a-posteriori correction that can capture the effect of honeycomb structures on seal discharge by accounting for changes in momentum and flow area.