By electrospinning liquid crystals coaxially inside a polymer sheath, responsive fibers with application potential, e.g., in wearable sensors can be produced. We conduct a combined scanning electron/polarizing microscopy study of such fibers, concluding that a match between the properties of the sheath solution and that of the core fluid is vital for achieving well‐formed and well‐filled fibers. Problems that may otherwise arise are fibers that are continuously filled, but partially collapsed; or fibers in which the core breaks up into droplets due to a mismatch in elongational viscosity between inner and outer fluids.