The metastatic cascade includes a blood circulation step for cells detached from the primary tumor. This stage involves significant shear stress as well as large and fast deformation as the cells circulate through the microvasculature. These mechanical stimuli are well reproduced in microfluidic devices. However, the recovery dynamics after deformation is also pivotal to understand how a cell can pass through the multiple capillary constrictions encountered during a single hemodynamic cycle. The microfluidic system developed in this work allows single cell recovery to be studied under flow-free conditions following pressure-actuated cell deformation inside constricted microchannels. We used three breast cancer cell lines - namely MCF-7, SK-BR3 and MDA-MB231 - as cellular models representative of different cancer phenotypes. Changing the size of the constriction allows exploration of moderate to strong deformation regimes, the latter being associated with the formation of plasma membrane blebs. In the regime of moderate deformation, all cell types display a fast elastic recovery behavior followed by a slower viscoelastic regime, well described by a double exponential decay. Among the three cell types, cells of the mesenchymal phenotype, i.e. the MDA-MB231 cells, are softer and the most fluid-like, in agreement with previous studies. Our main finding here is that the fast elastic recovery regime revealed by our novel microfluidic system is under the control of cell contractility ensured by the integrity of the cell cortex. Our results suggest that the cell cortex plays a major role in the transit of circulating tumor cells by allowing their fast morphological recovery after deformation in blood capillaries.