Engineers looking to enhance the relevance of search results in Elasticsearch applications can leverage the Ranking Evaluation API to achieve better outcomes. The blog post emphasizes the importance of tuning search relevance, which involves optimizing combinations of data, data models, and query templates. Relevance tuning is inherently subjective and varies based on unique datasets and user expectations, making test-driven approaches crucial. The Ranking Evaluation API, introduced in Elasticsearch version 6.2, allows engineers to measure search quality using information retrieval metrics like precision and mean reciprocal rank. To utilize this tool, engineers must gather a representative sample of queries and relevance judgments for evaluation. The process involves iteratively adjusting queries and configurations to improve search quality, ensuring that the system meets quality standards. The post also advises periodic re-evaluation as changes in data and user behavior can influence relevancy, and encourages feedback on the process.