Majorana neutrino electromagnetic properties are studied through neutral current coherent neutrino-nucleus scattering. We focus on the potential of the recently planned COHERENT experiment at the Spallation Neutron Source to probe muon-neutrino magnetic moments. The resulting sensitivities are determined on the basis of a chi^2 analysis employing realistic nuclear structure calculations in the context of the quasi-particle random phase approximation. We find that they can improve existing

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... by half an order of magnitude. In addition, we show that these facilities allow for Standard Model precision tests in the low energy regime, with a competitive determination of the weak mixing angle. Finally, they also offer the capability to probe other electromagnetic neutrino properties, such as the neutrino charge-radius. We illustrate our results for various choices of experimental setup and target material.