This contribution presents some recent results concerning the development of computer-aided design methods aimed at the protection of museum exhibits of predominantly globular shape, such as vases and cups. Some critical reflections are also proposed concerning the elaboration of a roadmap for the applicability of digital and computational technologies of the typology currently investigated, framed within the context of a model problem inspired by the case study of the protection of the Millefiori Cup, a first-century AD glass artifact of the Vesuvian area exhibited at the Naples National Archaeological Museum. Previous studies have shown that, despite its geometric simplicity, the rolling heavy half-disk model can effectively capture fundamental features of the post-impulse dynamics of freestanding globular objects and can be applied in the assessment of the vulnerability of museum artifacts to dynamic environmental excitations. Herein an extension is presented of the half-disk to the case of a semi-elliptical body undergoing free oscillations. The semi-ellipse retains the modeling advantages of the half-disk—such as avoiding indeterminacies caused by impacts on non-convex edges—while providing a more accurate geometric representation of real-world globular artifacts encompassing the variation of osculating circles. A Lagrangian formulation is developed, incorporating a constraint of pure rolling with no sliding, and the resulting nonlinear equations of motion are solved using time discretization and midpoint collocation.