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Ghost imaging has recently been successfully achieved in the X-ray regime. Due to the penetrating power of X-rays this immediately opens up the possibility of ghost-tomography. No research into this topic currently exists in the literature. Here, we present adaptations of conventional X-ray tomography techniques to this new ghost-imaging scheme. Several numerical implementations for tomography through X-ray ghost-imaging are considered. Specific attention is paid to schemes for reducing the noise-like artefacts of the resulting tomographic reconstruction, issues related to dose fractionation, and considerations regarding the ensemble of illuminating masks used for ghost-imaging. Each theme is explored through a series of numerical simulations, and several suggestions offered for practical realisations of ghosttomography.