This paper presents a spiking neuro-evolutionary system which implements memristors as neuromodulatory connections, i.e. whose weights can vary during a trial. The evolutionary design process exploits parameter self-adaptation and a constructionist approach, allowing the number of neurons, connection weights, and inter-neural connectivity pattern to be evolved for each network. We demonstrate that this approach allows the evolution of networks of appropriate complexity to emerge whilst exploiting the memristive properties of the connections to reduce learning time. We evaluate two phenomenological real-world memristive implementations against a theoretical “linear memristor”, and a system containing standard connections only. Our networks are evaluated on a simulated robotic navigation task.