Increasing high-impact, low-probability (HILP) disruptions require a paradigm shift in emergency power for critical infrastructure (CI), moving away from traditional cost-driven assessments toward physical resilience. To address this gap, this article develops a resilience-oriented screening framework to prequalify energy technologies (including CHP and CCHP) for CI facing prolonged outages. Diverging from pure economic optimization, the methodology prioritizes survivability criteria: islanding readiness, black-start capability, fuel autonomy, multivector energy coverage, implementation feasibility, and operational safety. A hospital serves as the reference CI due to its rigorous demand for simultaneous electricity, heat, cooling, and process loads. The framework employs a two-stage procedure: a Stage I go/no-go boundary filter and a Stage II weighted scoring matrix. This methodology evaluates a broad technology basket encompassing gas, biogas, and biomass CHP, CCHP with absorption cooling, hybrid CHP/BESS, RES+BESS, and diesel generators. Rather than providing a definitive techno-economic ranking, this study establishes a transparent, replicable front-end engineering tool. Ultimately, the results define boundary conditions for prequalifying multivector energy architectures, creating a foundation for future modeling and dynamic simulations of CI microgrids.