Multimodal large language models (MLLMs) achieve ever-stronger performance on visual-language tasks. Even as traditional visual question answering (VQA) benchmarks approach saturation, reliable deployment requires satisfying low error tolerances in real-world, out-of-distribution (OOD) scenarios. Precisely, selective prediction aims to improve coverage, i.e. the share of inputs the system answers, while adhering to a user-defined risk level. This is typically achieved by assigning a confidence score to each answer and abstaining on those that fall below a certain threshold. Existing selective prediction methods estimate implicit confidence scores, relying on model internal signals like logits or hidden representations, which are not available for frontier closed-sourced models. To enable reliable generalization in VQA, we require reasoner models to produce localized visual evidence while answering, and design a selector that explicitly learns to estimate the quality of the localization provided by the reasoner using only model inputs and outputs. We show that SIEVES (Selective Prediction through Visual Evidence Scoring) improves coverage by up to three times on challenging OOD benchmarks (V* Bench, HR-Bench-8k, MME-RealWorld-Lite, VizWiz, and AdVQA), compared to non-grounding baselines. Beyond better generalization to OOD tasks, the design of the SIEVES selector enables transfer to proprietary reasoners without access to their weights or logits, such as o3 and Gemini-3-Pro, providing coverage boosts beyond those attributable to accuracy alone. We highlight that SIEVES generalizes across all tested OOD benchmarks and reasoner models (Pixel-Reasoner, o3, and Gemini-3-Pro), without benchmark- or reasoner-specific training or adaptation. Code is publicly available at https://github.com/hector-gr/SIEVES .