Visual servoing with self-supervised Vision Transformer (ViT) features enables training-free robotic positioning with strong generalization, but faces a fundamental trade-off between robustness and precision. Coarse patch-level descriptors provide stable correspondences yet limit positioning accuracy. Increasing image resolution improves precision but yields only marginal robustness gains - under perturbation, high-resolution processing improves convergence success rate from 76.6% to just 81.0% despite 12x more ViT patches. Therefore, we propose Adaptive Resolution Tiling Visual Servoing (ART-VS), a two-phase method that adapts feature granularity to servoing progress: a coarse phase at native ViT resolution for stable alignment, then a tiled high-resolution phase that restricts matching to local neighborhoods improving positioning accuracy. Without any task-specific training, ART-VS achieves 95.4% convergence under perturbation, outperforming standard and full-resolution ViT-based servoing by 18.8 and 14.4 percentage points. Over the former it reduces positioning error by 53%, while running at over 10x higher speed and 27% lower VRAM than the latter. We validate ART-VS across three ViT backbones and demonstrate real-world category-level grasping of unseen object instances, achieving 95/100 on transparent bottles and 98/100 on shoes. Code available under https://art-vs.github.io/.

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