Distributed sensing by cooperative drone swarms is crucial for several Smart City applications, such as traffic monitoring and disaster response. Using an indoor lab with inexpensive drones, a testbed supports complex and ambitious studies on these systems while maintaining low cost, rigor, and external validity. This paper introduces the Multi-drone Sensing Experimentation Testbed (M-SET), a novel platform designed to prototype, develop, test, and evaluate distributed sensing with swarm intelligence. M-SET addresses the limitations of existing testbeds that fail to emulate collisions, thus lacking realism in outdoor environments. By integrating a collision avoidance method based on a potential field algorithm, M-SET ensures collision-free navigation and sensing, further optimized via a multi-agent collective learning algorithm. Extensive evaluation demonstrates accurate energy consumption estimation and a low risk of collisions, providing a robust proof-of-concept. New insights show that M-SET has significant potential to support ambitious research with minimal cost, simplicity, and high sensing quality.