Robust fitting of geometric models is a fundamental task in many computer vision pipelines. Numerous innovations have been produced on the topic, from improving the efficiency and accuracy of random sampling heuristics to generating novel theoretical insights that underpin new approaches with mathematical guarantees. However, one aspect of robust fitting that has received little attention is energy efficiency. This performance metric has become critical as high energy consumption is a growing concern for AI adoption. In this paper, we explore energy-efficient robust fitting via the neuromorphic computing paradigm. Specifically, we designed a novel spiking neural network for robust fitting on real neuromorphic hardware, the Intel Loihi 2. Enabling this are novel event-driven formulations of model estimation that allow robust fitting to be implemented in the unique architecture of Loihi 2, and algorithmic strategies to alleviate the current limited precision and instruction set of the hardware. Results show that our neuromorphic robust fitting consumes only a fraction (15%) of the energy required to run the established robust fitting algorithm on a standard CPU to equivalent accuracy.