The goal of this work was to use an undersampled, dual-plane centre-out radial sampling acquisition pulse sequence, with off-resonance reception, to localize fiducial markers with reduced acquisition time. Two iterative reconstruction techniques, conjugate gradient CG-SENSE and the variational penalty Total Generalized Variation (TGV), were investigated to minimize the undersampling artifacts in off-resonant radial imaging. Simulations of a field perturber were performed at sub-millimeter resolution and reconstructed to display signal pileups that can be radially compressed towards the geometric centre of the perturber for high contrast visualization, but contrast is non-recoverable as the echo time increases. A cylindrical platinum fiducial marker, placed in a phantom parallel and perpendicular to the B0-field was imaged with a short-TE half-echo readout. Contrast-to-Noise (CNR) between the signal of the fiducial its adjacent surrounding shell and half-maximum area were used to compare reconstruction methods and undersampling factors. For single slice acquisitions centred about the fiducial, each slice can be performed in as little as 2.8s. The total acquisition time to localize the fiducial marker in a phantom was reduced to 73s by undersampling (R=8) 37 axial and 15 coronal slices, effectively encoding 1.4s/slice. The noise present in undersampled images, for both scan planes and fiducial orientations, decreased significantly using TGV and CG-SENSE reconstructions, with TGV displaying better spatial resolution from reduced half-maximum area.