Biological electromagnetic fields arise throughout all tissue depths and types, and correlate with physiological processes and signalling in organs of the body. Most of the methods for monitoring these fields are either highly invasive or spatially coarse. Here, we show that implantable active coil-based transducers that are detectable via magnetic resonance imaging enable the remote sensing of biological fields. These devices consist of inductively coupled resonant circuits that change their properties in response to electrical or photonic cues, thereby modulating the local magnetic resonance imaging signal without the need for onboard power or wired connectivity. We discuss design parameters relevant to the construction of the transducers on millimetre and submillimetre scales, and demonstrate their in vivo functionality for measuring time-resolved bioluminescence in rodent brains. Biophysical sensing via microcircuits that leverage the capabilities of magnetic resonance imaging may enable a wide range of biological and biomedical applications.