Inspired by the discovery of superconductivity in moiré materials with isolated narrow bandwidth electronic bands, here we analyze critically the question of what is the maximum attainable Tc in interacting flat-band systems. We focus specifically on the low-energy effective theory, where the density-density interactions are projected to the set of partially filled flat bands. The resulting problem is inherently nonperturbative, where the standard mean-field approximation is not applicable. Here we develop further our recent Schrieffer-Wolf transformation based approach [PNAS 120, e2217816120 (2023)0027-842410.1073/pnas.2217816120] to compute the effective electromagnetic response and the superconducting phase-stiffness in terms of "projected"gauge transformations and extend the formalism to compute the stiffness for excitonic superfluids. Importantly, our method requires neither any "Wannierization"for the narrow bands of interest, regardless of their (non)topological character, nor any knowledge of an underlying pairing symmetry, and can be set up directly in momentum-space. We use this formalism to derive upper bounds on the phase stiffness for sign-problem-free models, where their values are known independently from numerically exact quantum Monte Carlo computations. We also illustrate the analytical structure of these bounds for the superconducting and excitonic phase-stiffness for perfectly flat bands with Landau-level-like wave functions. © 2024 American Physical Society.