In satellite applications, user queries often take the form of open-ended natural language, extending beyond a fixed set of predefined categories. This open-vocabulary nature poses significant challenges for retrieving relevant image tiles, as the retrieval system must generalize to a wide range of unseen objects and concepts. While vision-language models (VLMs) such as CLIP are widely used for text-image retrieval, even fine-tuned variants often struggle to accurately align such queries with satellite imagery. To address this, we propose Open-SAT, a training-free query embedding refinement algorithm that operates at inference time to improve alignment between user queries and satellite image content. Open-SAT uses VLMs to compute embeddings for image tiles, which are stored in a vector database for efficient retrieval. At query time, it leverages Large Language Models (LLMs) to refine the text embeddings by incorporating contextual information about objects of interest and their surroundings. A threshold-free retrieval mechanism further enhances accuracy and efficiency. Experimental results in three public benchmarks demonstrate that Open-SAT improves the F1 score by up to 16.04%, while retrieving a comparable number of image tiles. These results demonstrate the effectiveness of Open-SAT in open-vocabulary satellite image retrieval, leveraging LLM guidance without the need for additional training or supervision.