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In this article, the possibilities and limitations of proximity lithography with extreme ultraviolet (EUV) radiation are explored theoretically and experimentally. Utilizing partially coherent EUV radiation with a wavelength of 10.88 nm from a Xe/Ar discharge plasma EUV source, proximity patterning of various nanoantenna arrays has been performed. The experimental results are compared with the results of numerical scalar diffraction simulations, and it is shown that proximity printing in the Fresnel diffraction mode can enable production of high-resolution features even with lower resolution masks, successfully demonstrating sub-30 nm edge resolution in the resist. The potential of the method is explored by simulation of the patterning through circular and triangular apertures as well as through bowtie antenna patterns, with the results suggesting that precise control of the proximity gap and the exposure dose together with simulation-supported mask design optimizations may allow for a wide variety of high-resolution structures to be printed through relatively simple transmission masks. The method is especially suited for high-performance manufacturing of submicrometer sized nanophotonic arrays.