X-ray computed tomography (CT) is a versatile nondestructive inspection method, owing in part to the wide range of sample sizes and achievable spatial resolution. X-ray microscopy CT is a category of CT that combines X-ray imaging with microscope optics to perform high-resolution submicron measurements in a compact form-factor. However, the high resolution and the form-factor incur certain non-trivial limits on this imaging modality. Among the most critical restrictions is the limited physical size of the field of view (FoV), which hinders high-resolution inspection of wide or tall samples. Additionally, microscope optics and the physics of X-ray imaging exacerbate this limit by introducing distortions and loss of spatial resolution. This work deals with the analysis and reduction of the physical and optical limits in submicron X-ray microscopy CT. Techniques of both lateral and axial FoV extension are examined to address the physical limits of the FoV, and the optical and imaging limits, which have the potential to jeopardize these techniques, are addressed. A multi-stage alignment approach and seamless blending strategy are implemented for fast and effective combination of CT volumes, facilitating axial FoV extension. For lateral extension, limits of the well-known offset-scan measurement protocol are evaluated and reported. A robust and affordable method is implemented for correcting radial distortion of microscope lenses. Finally, two methods are adapted and implemented for estimating the point spread function (PSF) of the CT scanner, a crucial factor of the spatial resolution of X-ray microscopes, and a powerful tool for image enhancement through deconvolution. The methods and analyses discussed in this work form a suite of techniques for both understanding and surpassing the limits of X-ray microscopy CT, which increases the utility of this modality while creating a basis for further improvements of the image quality achievable on these devices.