This dataset contains the data used to create Figures 3 to 7 in the paper, "Confinement loss of anti-resonant capillaries with curved boundaries". The different Figures, and the related datasets, represents the confinement loss of hollow-core fibres with either a solid core surround or an anti-resonant core surround and with a wide range of different geometrical shapes and structural parameters. In all cases, the results are compared with the confinement loss of reference circular fibre structures. Data for Figures 3 to 5 is calculated with an in-house boundary element code. Data for Figures 6 and 7 is calculated using the commercial finite-element solver, COMSOL Multiphysics.