What is the most expensive part of quantum device characterization? Clearly, the answer is quantum process tomography. However, especially for noisy intermediate-scale quantum (NISQ) computers, a comprehensive understanding of the noisy quantum dynamics is essential in interpreting the computational output. In this work, we introduce an efficient method – Procrustes tomography – that outperforms established methods in a number of aspects. After a pedagogical and constructive introduction, we demonstrate the utility of the method for representative examples of noisy quantum channels.