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In thermionic energy converters, the absolute efficiency can be increased up to 40% if space-charge losses are eliminated by using a sub-10-µm gap between the electrodes. One practical way to achieve such small gaps over large device areas is to use a stiff and thermally insulating spacer between the two electrodes. We report on the design, fabrication and characterization of thin-film alumina-based spacers that provided robust 3–8 μm gaps between planar substrates and had effective thermal conductivities less than those of aerogels. The spacers were fabricated on silicon molds and, after release, could be manually transferred onto any substrate. In large-scale compression testing, they sustained compressive stresses of 0.4–4 MPa without fracture. Experimentally, the thermal conductance was 10–30 mWcm⁻²K⁻¹and, surprisingly, independent of film thickness (100–800 nm) and spacer height. To explain this independence, we developed a model that includes the pressure-dependent conductance of locally distributed asperities and sparse contact points throughout the spacer structure, indicating that only 0.1–0.5% of the spacer-electrode interface was conducting heat. Our spacers show remarkable functionality over multiple length scales, providing insulating micrometer gaps over centimeter areas using nanoscale films. These innovations can be applied to other technologies requiring high thermal resistance in small spaces, such as thermophotovoltaic converters, insulation for spacecraft and cryogenic devices.