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Although reliable rechargeable batteries represent a key transformative technology for electric vehicles, portable electronics, and renewable energy, there are few nondestructive diagnostic techniques compatible with realistic commercial cell enclosures. Many battery failures result from the loss or chemical degradation of electrolyte. In this work, we present measurements through battery enclosures that allow quantification of electrolyte amount and composition. The study employs instrumentation and techniques developed in the context of zero-to-ultralow-field nuclear magnetic resonance (ZULF NMR), with optical atomic magnetometers as the detection elements. In contrast to conventional NMR methodology, which suffers from skin-depth limitations, the reduced resonance frequencies in ZULF NMR make battery housing and electrodes transparent to the electromagnetic fields involved. As demonstrated here through simulation and experiment, both the solvent and lithium-salt components of the electrolyte (LiPF6) signature could be quantified using our techniques. Further, we show that the apparatus is compatible with measurement of pouch-cell batteries.