Quantization is essential for reducing the computational cost and resource demand of large language models (LLMs). As the community pushes beyond 8‑bit quantization, 4‑bit formats such as MXFP4 and NVFP4 have been proposed. HiFloat4 (HiF4) uses a block‑floating‑point (BFP) scheme with a three‑level scaling hierarchy, providing a much larger dynamic range. While quantization dramatically cuts memory usage and speeds up inference, it often degrades accuracy, making calibration crucial to narrow the gap between low‑precision and full‑precision models. Existing calibration techniques are designed for integer formats (e.g., INT4) and do not support HiF4’s hierarchical BFP structure. This paper investigates three HiF4‑specific calibration approaches: HiGPTQ, HiAutoRound, and HiFlatQuant. Extensive experiments across various models and downstream tasks show that all three methods improve inference accuracy over direct HiF4 conversion, reducing the HiF4‑BF16 performance gap to less than 1% and outperforming the state‑of‑the‑art NVFP4 format in most cases.\n\nReview