Memristors are an emerging technology that enables artificial intelligence (AI) accelerators with high energy efficiency and radiation robustness — properties that are vital for the deployment of AI on-board spacecraft. However, space applications require reliable and precise computations, while memristive devices suffer from non-idealities, such as device variability, conductance drifts, and device faults. Thus, porting neural networks (NNs) to memristive devices often faces the challenge of severe performance degradation. In this work, we show in simulations that memristor-based NNs achieve competitive performance levels on on-board tasks, such as navigation & control and geodesy of asteroids. Through bit-slicing, temporal averaging of NN layers, and periodic activation functions, we improve initial results from around 0.07 to 0.01 and 0.3 to 0.007 for both tasks using RRAM devices, coming close to state-of-the-art levels (0.003−0.005 and 0.003, respectively). Our results demonstrate the potential of memristors for on-board space applications, and we are convinced that future technology and NN improvements will further close the performance gap to fully unlock the benefits of memristors.