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A software-supported systematic methodology for exploring and evaluating alternative 3D reconfigurable FPGA architectures is introduced. Two new software tools were developed: (i) a placement and routing tool for 3D FPGAs (3DPRO) and (H) a power/energy consumption estimation tool for such architectures (3DPower). Both of them are part of the new Design Framework, named 3D-MEANDER. We mainly focus our exploration on parameters that dominate the maximum operation frequency of the 3D FPGAs (i.e. vertical interconnections, number of layers, etc.). We evaluate the efficiency of the proposed methodology by making an exhaustive exploration for device delay, power consumption and utilized number of vertical connections for alternative 3D interconnection schemes. Experimental results demonstrate the effectiveness of our methodology, considering the 20 largest MCNC benchmarks. We achieve an average decrease in the delay, the wire length, and the energy consumption of 27%, 26%, and 34%, respectively, as compared to traditional 2D FPGAs, considering 3D architectures with 50% and 70% of fabricated vias. Also, we proved that actually-utilized via links are practically independent from the number of fabricated vias of a 3D FPGA architecture.