Machine-learning surrogates predict composite properties but report no calibrated reliability and may violate physics. Bound-constrained conformal prediction confines intervals to physical bounds but assumes them exact. This paper keeps the corridor as a hard constraint and characterizes what a decision-support system guarantees when it is wrong. If a fraction $\eta$ of responses lies outside the corridor, no admissible interval covers more than $1-\eta$, so the nominal level $1-\alpha$ is attainable only if $\eta \le \alpha$. A projection-aware calibration scores out-of-corridor points as infinitely nonconforming. Its marginal coverage is at least $1-\alpha -\eta {\pi }_{\infty }$ at every calibration size (${\pi }_{\infty }$ the fallback probability); its coverage across calibrations follows an exact Beta law. In the limit it reaches the nominal level whenever attainable; calibrate-then-clip loses up to $\eta$. For $\eta <\alpha$ the system thus delivers admissible intervals at the nominal level for a small, quantified width premium, with a feasibility verdict and a Shapley explanation. Across eight datasets it recovers the nominal level on a woven laminate with a misspecified rule-of-mixtures bound (90.3% against 85.6% for naive projection) and tracks the frontier under normative bounds the data contradict. Under exact Voigt–Reuss bounds it removes all violations and narrows intervals thirteen-fold. Width, paid inside the corridor, is the price.