Nonflammable solid-state electrolytes can potentially address the reliability and energy density limitations of lithium-ion batteries. Garnet-structured oxides such as Li7La3Zr2O12 (LLZO) are some of the most promising candidates for solid-state devices. Here, three-dimensional (3D) solid-state LLZO frameworks with low tortuosity pore channels are proposed as scaffolds, into which active materials and other components can be infiltrated to make composite electrodes for solid-state batteries. To make the scaffolds, we employed aqueous freeze tape casting (FTC), a scalable and environmentally friendly method to produce porous LLZO structures. Using synchrotron radiation hard X-ray microcomputed tomography, we confirmed that LLZO films with porosities of up to 75% were successfully fabricated from slurries with a relatively wide concentration range. The acicular pore size and shape at different depths of scaffolds were quantified by fitting the pore shapes with ellipses, determining the long and short axes and their ratios, and investigating the equivalent diameter distribution. The results show that relatively homogeneous pore sizes and shapes were sustained over a long range along the thickness of the scaffold. Additionally, these pores had low tortuosity and the wall thickness distributions were found to be highly homogeneous. These are desirable characteristics for 3D solid electrolytes for composite electrodes, in terms of both the ease of active material infiltration and also minimization of Li diffusion distances in electrodes. The advantages of the FTC scaffolds are demonstrated by the improved conductivity of LLZO scaffolds infiltrated with poly(ethylene oxide)/lithium bis(trifluoromethanesulfonyl)imide (PEO/LITFSI) compared to those of PEO/LiTFSI films alone or composites containing LLZO particles.