Purpose: To evaluate an algorithm for calibrationless parallel imaging to reconstruct undersampled parallel transmit field maps for the body and brain. Methods: Using synthetic data, body, and brain measurements of relative transmit maps, three different approaches to a joint transmit-receive low-rank tensor completion algorithm are evaluated. These methods included: (i) virtual coils using the product of receive and transmit sensitivities, (ii) joint-receiver coils that enforces a low rank structure across receive coils of all transmit modes, and (iii) transmit low rank (TxLR) that uses a low rank structure for both receive and transmit modes simultaneously. The performance of each are investigated for different noise levels and different acceleration rates on an 8-channel parallel transmit 7T system. Results: The virtual coils method broke down with increasing noise levels or acceleration rates greater than two producing RMS error greater than 0.1. The joint receiver coils method worked well up to acceleration factors of four, beyond which the RMS error exceeded 0.1. While TxLR enabled an eight-fold acceleration with most RMS errors remaining below 0.1. Conclusion: This work demonstrates that under-sampling factors of up to eight-fold are feasible for transmit array mapping and can be reconstructed using calibrationless parallel imaging methods.