Learning-based surrogates for alternating-current optimal power flow (AC-OPF) offer significant speed advantages for real-time power system operation, yet they often suffer from a lack of physical feasibility guarantees. Small prediction errors in neural networks can result in critical violations of AC power-flow equations and operational constraints, posing significant risks for practical deployment. This paper introduces a universal feasibility projection and certification (UFPC) framework designed to act as an architecture-agnostic trust layer for any neural OPF predictor. The framework employs a multi-stage hierarchical repair pipeline to transform arbitrary model outputs into physically valid operating points, ensuring strict adherence to network physics and engineering limits. To bridge the gap between fast inference and reliable operation, we further develop an explicit physics-based feasibility certificate that quantifies equality and inequality residuals alongside local numerical conditioning, enabling an automated decision logic to accept, refine, or invoke a conventional solver fallback. Extensive numerical experiments demonstrate that the proposed UFPC framework effectively enforces AC feasibility, provides reliable performance across diverse operating conditions, and maintains the computational efficiency required for real-time power system control.