Unmanned Aerial Vehicle (UAV) swarms exhibit strong potential for complex missions. However, there has been limited research on their behavior during search-and-track missions, particularly under sensing limitations. This study explores a leader–follower UAV swarm that performs a search-and-track mission in which sensing capabilities are concentrated on the leader UAV. In this scenario, the leader detects and tracks the target, while the follower drones operate with limited sensing and receive updates from the leader. Once the target is detected, the swarm transitions into a coordinated ring formation surrounding the target, with the leader guiding the overall ring formation. This study aimed to demonstrate how limited follower sensing affects the formation quality, response to target motion, and overall tracking performance. A simulation framework was developed to evaluate swarm behavior under sensing limitations. The results showed that effective tracking and encirclement can be achieved even when advanced sensing is concentrated on the leader, thereby demonstrating the potential of building scalable and cost-efficient UAV swarm systems.