Vision-language models (VLMs) enable open-ended visual question answering but remain prone to hallucinations. We present HEDGE, a unified framework for hallucination detection that combines controlled visual perturbations, semantic clustering, and robust uncertainty metrics. HEDGE integrates sampling, distortion synthesis, clustering (entailment- and embedding-based), and metric computation into a reproducible pipeline applicable across multimodal architectures. Evaluations on VQA-RAD and KvasirVQA-x1 with three representative VLMs (LLaVA-Med, Med-Gemma, Qwen2.5-VL) reveal clear architecture- and prompt-dependent trends. Hallucination detectability is highest for unified-fusion models with dense visual tokenization (Qwen2.5-VL) and lowest for architectures with restricted tokenization (Med-Gemma). Embedding-based clustering often yields stronger separation when applied directly to the generated answers, whereas NLI-based clustering remains advantageous for LLaVA-Med and for longer, sentence-level responses. Across configurations, the VASE metric consistently provides the most robust hallucination signal, especially when paired with embedding clustering and a moderate sampling budget (n ~ 10-15). Prompt design also matters: concise, label-style outputs offer clearer semantic structure than syntactically constrained one-sentence responses. By framing hallucination detection as a geometric robustness problem shaped jointly by sampling scale, prompt structure, model architecture, and clustering strategy, HEDGE provides a principled, compute-aware foundation for evaluating multimodal reliability. The hedge-bench PyPI library enables reproducible and extensible benchmarking, with full code and experimental resources available at https://github.com/Simula/HEDGE .