Initial work by Georgoulis, Tziotziou & Raouafi (ApJ, 759:1, 2012) on the estimation of the coronal relative magnetic helicity budget in solar active regions has been scrutinized in multiple occasions by comparison to ‘ground-truth’ calculations of the volume helicity using classical formulas, mainly in synthetic magnetic configurations. The so-called connectivity-based helicity / energy calculation method infers a coronal magnetic connectivity matrix without three-dimensional extrapolation or magnetohydrodynamical modeling and then calculates magnetic energy and relative helicity budgets on a discretized flux tube ensemble as per the inferred connectivity. We briefly report on the comparison of the method with classical ‘finite volume’ methods applied to real solar active regions, in which the coronal magnetic field has been inferred by nonlinear force-free extrapolations. Then we describe a recent extension of this line on work that relies on the fundamental conservation principle for the magnetic helicity to infer a worst-case axial magnetic field (Bz) for solar and stellar coronal mass ejections (CMEs) at various locations in the helio-/astro-sphere. Besides connecting the flaring with the CME manifestations in the eruptive active regions, this approach can contribute to an improved understanding of stellar forcing on exoplanetary systems and has, in fact, led to the recent derivation of an atmosphere sustainability constraint for terrestrial exoplanets.