Inverse opals are most widely used as photonic crystals for ultraviolet, optical and infrared applications.These highly interconnected porous structures are also attractive for applications such as sensors, fuel cells, filters, and catalysts. At the same time, engineers are aiming for lightweight structures with optimized mechanical strength, often inspired by nature’s cellular materials with foam-like structures such as sponges, trabecular bone or plant parenchyma. The resultant optimized strut-based structures have shown high stiffness- and compressive strength-to-weight ratios, but can suffer from strut buckling and a lack of mass production techniques. Here we show that mechanical metamaterials based on ceramic inverse opaline structures with densities in the range of 330-910 kg/m3 are not only suitable as photonic crystals but also show better stiffness- and compressive strength-to-weight ratios compared to micro-fabricated optimized strut-based structures, but lower than carbon nanoframes fabricated by interference lithography. Pure silica inverse opal structures and silica inverse opals whose pores have been internally coated by a thin TiO2-layer have been fabricated and their structural and mechanical behaviour was investigated. Our experimental results, supported by numerical simulations, show that these arch-shaped porous structures can outperform both strut-based and honeycomb structures due to their nearly isotropic mechanical response.