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SRON is developing an electronic read-out system for an array of Transition-Edge Sensors (TES) which combines the techniques of Frequency Domain Multiplexing (FDM) with Base-Band FeedBack (BBFB). Its potential astronomical applications are in the read-out of soft X-ray microcalorimeters of the XMS instrument on the International X-ray Observatory (IXO) and the far-IR bolometers of the SAFARI instrument on the Japanese-European mission SPICA. In this paper we focus on the experimental verification of the system, demonstrating for 16 pixels that simultaneous read-out does not degrade the noise performance, and that crosstalk between pixels is close to the requirements for IXO. A detailed analysis of the BBFB system is presented, identifying its limitations and routes for improvement to the levels required for implementation on both missions.