We present a spectroscopic method that extends the ability to determine magnetic-field amplitudes to a diagnostically difficult regime for which the Zeeman-split patterns are not resolvable. In the new approach, the magnetic field is inferred  from the comparison of the line-shapes of different fine-structure components of the same multiplet, which practically have the same Stark and Doppler broadenings, but different magnetic-field-induced contributions to the line shapes. Since this method does not rely on the polarization properties of the radiation, it is particularly useful when the magnetic-field direction changes significantly in the region viewed or during the time of observation. Even when the magnetic field does have a preferred direction and polarization techniques are applicable, the new method has practical advantageous in cases where the Zeeman pattern is completely smeared out due to the dominance of the Stark and Doppler broadenings. Measurements performed for aluminum ablated plasma (n_e ~ 10¹⁶ – 10¹⁸ cm^-3) in externally applied magnetic fields (up to 25 T) demonstrate the usefulness and reliability of the new method.