Variability of the geomagnetic field induces anomalous Geomagnetically Induced Currents (GICs) in grounded conducting infrastructure. GICs represent a serious space weather hazard, but are not often measured directly and the rate of change of the magnetic field is often used as a proxy. We assess the correlation between the rate of change of the magnetic field and GICs during Sudden Commencements (SCs), at a location in New Zealand. We observe excellent correlations (r2 ∼ 0.9) between the maximum one-minute rate of change of the field and maximum GIC. Nonetheless, though SCs represent a relatively simple geomagnetic signature, we find that the correspondence systematically depends on several factors. If the SC occurs when New Zealand is on the dayside of the Earth then the magnetic changes are linked to 30% greater GICs than if New Zealand is on the nightside. We investigate, finding that the orientation of the strongest magnetic deflection is important: changes predominantly in the east-west direction drive 36% stronger GICs. Dayside SCs are also associated with faster maximum rates of change of the field at 1 s resolution. Therefore, while the maximum rates of change of the magnetic field and GICs are well correlated, the orientation and sub-one-minute resolution details of the field change are important to consider when estimating the associated currents. Finally, if the SC is later followed by a geomagnetic storm then a given rate of change of the magnetic field is associated with 22% larger GICs, compared to if the SC is isolated.