Open experimentation with operational Mobile Broadband (MBB) networks in the wild is currently a fundamental requirement of the research community in its endeavor to address the need of innovative solutions for mobile communications. Even more, there is a strong need for objective data about stability and performance of MBB (e.g., 3G/4G) networks, and for tools that rigorously and scientifically assess their status. In this paper, we introduce the MONROE measurement platform: an open access and flexible hardware-based platform for measurements and custom experimentation on operational MBB networks. The MONROE platform enables accurate, realistic and meaningful assessment of the performance and reliability of 11 MBB networks in Europe. We report on our experience designing, implementing and testing the solution we propose for the platform. We detail the challenges we overcame while building and testing the MONROE testbed and argue our design and implementation choices accordingly. We describe and exemplify the capabilities of the platform and the wide variety of experiments that external users already perform using the system