Molecules with an odd number of electrons typically display paramagnetic behaviour in a uniform magnetic field. Single-molecule toroics—a family of open shell lanthanide complexes—instead display an unprecedented vanishing magnetization. The anomaly is reconciled by degenerate quantum states where electron spins and orbital currents give rise to time-odd and space-odd magnetic vortices known as toroidal moments, that carry a vanishing magnetic dipole. Resilient to stray magnetic fields and susceptible to electric manipulation, toroidal moments have attracted interest for spintronic, magnonic, and photonic applications. While macroscopic toroidal moments feature in some extended systems, molecular toroidal states have yet to be observed, as it remains unclear how existing experimental set-ups could split degenerate states carrying counter-rotating vortices. We propose a realistic pulsed radiation protocol to polarise and observe molecular toroidal moments in a class of MDy${}_6$ (M = Al${}^{3+}$, Cr${}^{3+}$) molecules with coupled Dy${}_3$ toroidal moieties. Three resonant MW-pulses—delivered sequentially or simultaneously—selectively and coherently transfer population to a long-lived toroidally-polarised state whose ensuing magneto-electric properties provide a read-out mechanism. An order-of-magnitude estimate of the bulk magnetic dipole induced in toroidally polarised AlDy${}_6$ by an externally applied electric field validates detectability by $\mu$SQUID magnetometry, even in the presence of molecular disorder. Our results provide a strategy to measure and coherently manipulate toroidal states in molecular systems, which is expected to trigger applications of molecular toroidal states to quantum technologies.