The smallest eigenvalues of the Hodge–Laplacian govern key stability properties of partial differential equations. Computable lower bounds for these eigenvalues immediately provide computable upper bounds for the constants appearing in Poincaré, Friedrichs, and Weber-type inequalities. This talk surveys recent advances in deriving such estimates in a range of settings, from convex and star-shaped domains to local patches and fully general triangulated domains. The emphasis is on explicit, rigorous, and practically computable bounds. This is joint work with Théophile Chaumont-Frelet and Martin Vohralík.