Measuring large electrical resistances forms an essential part of common applications such as insulation testing but suffers from a fundamental problem: the larger the resistance, the less sensitive is a canonical ohmmeter. Here, we develop a conceptually different electronic sensor by exploiting the topological properties of non-Hermitian matrices, the eigenvalues of which can show an exponential sensitivity to perturbations. The ohmmeter is realized in a multiterminal linear electronic circuit with a non-Hermitian conductance matrix, where the target resistance plays the role of the perturbation. We inject multiple currents and measure a single voltage in order to directly obtain the value of the resistance. The relative accuracy of the device increases exponentially with the number of terminals and for large resistances outperforms a standard measurement by over an order of magnitude. Our work hopefully paves the way toward leveraging non-Hermitian conductance matrices in high-precision sensing.