Maritime port inspection plays a critical role in ensuring safety, regulatory compliance, and operational efficiency in complex maritime environments. However, existing inspection methods often rely on manual operations and conventional computer vision techniques that lack scalability and contextual understanding. This study introduces a novel integrated engineering framework that utilizes the synergy between Large Language Models (LLMs) and Vision Language Models (VLMs) to enable autonomous maritime port inspection using cooperative aerial and surface robotic platforms. The proposed framework replaces traditional state-machine mission planners with LLM-driven symbolic planning and improved perception pipelines through VLM-based semantic inspection, enabling context-aware and adaptive monitoring. The LLM module translates natural language mission instructions into executable symbolic plans with dependency graphs that encode operational constraints and ensure safe UAV-USV coordination. Meanwhile, the VLM module performs real-time semantic inspection and compliance assessment, generating structured reports with contextual reasoning. The framework was validated using the extended MBZIRC Maritime Simulator with realistic port infrastructure and further assessed through real-world robotic inspection trials. The lightweight on-board design ensures suitability for resource-constrained maritime platforms, advancing the development of intelligent, autonomous inspection systems. Project resources (code and videos) can be found here: https://github.com/Muhayyuddin/llm-vlm-fusion-port-inspection