This paper proposes a norm-based admissibility criterion formulated in the frequency domain for evaluating whether translational and rotational motion amplitudes of a ship moored at a quay remain within operational limits prescribed by port authorities. The approach is built on a linear six-degree-of-freedom model that includes hydrodynamic added-mass and radiation-damping effects, wave excitation forces, and aerodynamic wind loads, as well as linearized reactions of mooring lines and quay fenders, including an equivalent viscous representation of hull–fender friction. Instead of explicitly inverting the full system matrix to compute the complete response, the admissibility assessment is derived from row-wise norm bounds of the frequency-domain system, yielding a computationally efficient admissibility criterion for compliance with motion limits. The criterion naturally enables a port-oriented decision index and an operational safety margin that can be evaluated for each degree of freedom and used to compare alternative mooring arrangements. Numerical verification is performed for a bulk carrier under storm wave excitation and different loading conditions, demonstrating the sensitivity of admissibility to mooring geometry and pretension. The results confirm that the proposed criterion provides a practical engineering tool for rapid go/no-go decisions regarding cargo operations and supports the selection of mooring arrangements that improve operational robustness under adverse environmental loading conditions. In addition, a Monte Carlo-based uncertainty analysis is performed to evaluate the robustness of the proposed admissibility criterion with variable mooring stiffness and damping parameters. The proposed criterion is intended as a rapid engineering screening tool to complement conventional frequency-domain response analysis.