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Nuclear magnetic resonance (NMR) can probe the local structure and dynamic properties of liquids and solids, making it one of the most powerful and versatile analytical methods available today. However, its intrinsically low sensitivity precludes NMR analysis of very small samples-as frequently used when studying isotopically labelled biological molecules or advanced materials, or as preferred when conducting high-throughput screening of biological samples or 'lab-on-a-chip' studies. The sensitivity of NMR has been improved by using static micro-coils, alternative detection schemes and pre-polarization approaches. But these strategies cannot be easily used in NMR experiments involving the fast sample spinning essential for obtaining well-resolved spectra from non-liquid samples. Here we demonstrate that inductive coupling allows wireless transmission of radio-frequency pulses and the reception of NMR signals under fast spinning of both detector coil and sample. This enables NMR measurements characterized by an optimal filling factor, very high radio-frequency field amplitudes and enhanced sensitivity that increases with decreasing sample volume. Signals obtained for nanolitre-sized samples of organic powders and biological tissue increase by almost one order of magnitude (or, equivalently, are acquired two orders of magnitude faster), compared to standard NMR measurements. Our approach also offers optimal sensitivity when studying samples that need to be confined inside multiple safety barriers, such as radioactive materials. In principle, the co-rotation of a micrometre-sized detector coil with the sample and the use of inductive coupling (techniques that are at the heart of our method) should enable highly sensitive NMR measurements on any mass-limited sample that requires fast mechanical rotation to obtain well-resolved spectra. The method is easy to implement on a commercial NMR set-up and exhibits improved performance with miniaturization, and we accordingly expect that it will facilitate the development of novel solid-state NMR methodologies and find wide use in high-throughput chemical and biomedical analysis.