We introduce a numerical package FORward Experiment SEnsitivity Estimator, or FORESEE, that can be used to simulate the expected sensitivity reach of experiments placed in the far-forward direction from the proton-proton interaction point. The simulations can be performed for $14$ TeV collision energy characteristic for the LHC, as well as for larger energies: $27$ and $100$ TeV. In the package, a comprehensive list of validated forward spectra of various SM species is also provided. The capabilities of FORESEE are illustrated for the popular dark photon and dark Higgs boson models, as well as for the search for light up-philic scalars. For the dark photon portal, we also comment on the complementarity between such searches and dark matter direct detection bounds. Additionally, for the first time, we discuss the prospects for the LLP searches in the proposed future hadron colliders: High-Energy LHC (HE-LHC), Super proton-proton Collider (SppC), and Future Circular Collider (FCC-hh).
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