This paper deals with wave energy conversion in shallow water, analyzing the performance of two different oscillating-body systems. The first one is a heaving float, which is a system known in the literature. The second one is obtained by coupling the heaving float with a surging paddle. In order to check the different behaviors of the multibody system and the single-body heaving float, physical models of the two systems have been tested in a wave flume, by placing them at various water depths along a sloping bottom. The systems have been tested with monochromatic waves. For each water depth, several tests have been performed varying the geometrical and mechanical parameters of the two systems, in order to find their best configurations. It has been found that the multibody system is more energetic when the float and the paddle are close to each other. Capture width ratio has been found to significantly vary with water depth for both systems: in particular, capture width ratio of the heaving float (also within the multibody system) increases as water depth increases, while capture width ratio of the paddle (within the multibody system) increases as water depth decreases. At the end, the capture width ratio of the multibody system is almost always higher than that of the heaving float, and it increases as water depth increases on average; however, the multibody advantage over single body is significant for water depth less than the characteristic dimension of the system, and decreases as water depth increases.