X-ray tomography can be used to study the structure of whole cells in close to their native state. Ptychographic Fresnel coherent diffractive imaging (FCDI) holds particular promise for high-resolution tomographic imaging with quantitative phase sensitivity. To avoid the common missing wedge problem in tomography, cells can be mounted in thin glass capillaries that allow access to the full 180° angular field. However, soft x-rays, which are preferred for cellular imaging, interact strongly with capillaries, sometimes leading to violation of the usual assumptions for coherent diffractive imaging (CDI) and introducing artifacts (i.e., phase wrapping) in the reconstructed images. Here, we describe a method of applying ptychographic FCDI to obtain quantitative x-ray phase images of whole eukaryotic cells mounted in capillaries. The approach eliminates phase-wrapping artifacts due to thick capillaries without the deterioration in image quality that occurs at shallow angles of incidence when using planar mounting schemes. This technique makes it possible to apply CDI tomography to the study of various specimens that can be supported in capillaries and is compatible with established methods of cryogenic preparation.