Consumers are increasingly shopping online, and more and more datasets documenting consumer search are becoming available. While sequential search models provide a framework for utilizing such data, they present empirical challenges. A key difficulty arises from the inequality conditions implied by these models, which depend on multiple unobservables revealed during the search process and necessitate solving or simulating high-dimensional integrals for likelihood-based estimation methods. This paper introduces a novel representation of inequalities implied by a broad class of sequential search models, demonstrating that the empirical content of such models can be effectively captured through a specific partial ranking of available actions. This representation reduces the complexity caused by unobservables and provides a tractable expression for joint probabilities. Leveraging this insight, we propose a GHK-style simulation-based likelihood estimator that is simpler to implement than existing ones. It offers greater flexibility for handling incomplete search data, incorporating additional ranking information, and accommodating complex search processes, including those involving product discovery. We show that the estimator achieves robust performance while maintaining relatively low computational costs, making it a practical and versatile tool for researchers and practitioners.