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Abstract Higgs coupling deviations from Standard Model predictions contain information about two scales of Nature: that of new physics responsible for the deviation, and the scale where new bosons must appear. The two can coincide, but they do not have to. The scale of new bosons can be calculated by going beyond an effective field theory description of the coupling deviation. We compute model-independent upper bounds on the scale of new bosons for deviations in Higgs to WW and ZZ couplings, finding that any measured deviation at present or future colliders requires the existence of new bosons within experimental reach. This has potentially interesting implications for naturalness.