Single-cell chromosome conformation capture approaches are revealing the extent of cell-to-cell variability in the organization and packaging of genomes. These single-cell methods, unlike their multi-cell counterparts, allow straightforward computation of realistic chromosome conformations that may be compared and combined with other, independent, techniques to study 3D structure. Here we discuss how single-cell Hi-C and subsequent 3D genome structure determination allows comparison with data from microscopy. We then carry out a systematic evaluation of recently published single-cell Hi-C datasets to establish a computational approach for the evaluation of single-cell Hi-C protocols. We show that the calculation of genome structures provides a useful tool for assessing the quality of single-cell Hi-C data because it requires a self-consistent network of interactions, relating to the underlying 3D conformation, with few errors, as well as sufficient longer-range cis- and trans-chromosomal contacts.