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A primary goal of present and future colliders is measuring the Higgs couplings to Standard Model (SM) particles. Any observed deviation from the SM predictions for these couplings is a sign of new physics whose energy scale can be bounded from above by requiring tree-level unitarity. In this paper, we extend previous work on unitarity bounds from the Higgs cubic coupling to Higgs couplings to vector bosons and top quarks. We find that HL-LHC measurements of these couplings compatible with current experimental bounds may point to a scale that can be explored at the HL-LHC or a next-generation collider. Our approach is completely model-independent: we assume only that there are no light degrees of freedom below the scale of new physics, and allow arbitrary values for the infinitely many couplings beyond the SM as long as they are in agreement with current measurements. We also extend and clarify the methodology of this analysis, and show that if the scale of new physics is above the TeV scale, then the deviations can be described by the leading higher-dimension gauge invariant operator, as in the SM effective field theory.