Electrodes in high-energy all-solid-state lithium batteries are typically composites, consisting of mixtures of a Li storage material and a solid electrolyte. Ion transport in such composite electrodes plays an important role for battery performance. A key parameter characterizing effectiveness of ion transport is the tortuosity. While the tortuosity of separators and porous electrodes used in liquid-electrolyte batteries has been already investigated, there is a lack of data for electrodes of all-solid-state batteries. In this work, we present results for the tortuosity of a typical composite cathode, consisting of LiCoO2 active material particles and a sulfide-based solid electrolyte. To get values for tortuosity, two different approaches were followed. The first one is based on impedance spectroscopic measurements of the stationary Li+ current across the composite. The second approach combines three-dimensional reconstruction of the electrode structure based on focused ion-beam scanning electron microscopy with numerical simulations of ion transport in the reconstructed electrode. The presented results demonstrate a significant effect of residual voids in the composite electrode on the ion transport tortuosity. Careful attention should therefore be paid to the actual amount of void space formed during the preparation of composite electrodes as key component of all-solid-state batteries.