Field Programmable Gate Arrays (FPGAs) rely heavily on complex routing architectures. The routing structures use programmable switches and account for a significant share in the total area, delay and power consumption numbers. With the ability of being monolithically integrated with CMOS chips, Resistive Random Access Memories (RRAMs) enable high-performance routing architectures through the replacement of Static Random Access Memory (SRAM)-based programming switches. Exploiting the very low on-resistance state achievable by RRAMs as well as the improved tolerance to power supply reduction, RRAM-based routing multiplexers can be used to significantly reduce the power consumption of FPGA systems with no performance compromises. By evaluating the opportunities of ultra-low-power RRAM-based FPGAs at the system level, we see an improvement of 12%, 26% and 81% in area, delay and power consumption at a mature technology node.