Abstract: Operator models are regression algorithms between Banach spaces of functions and have become a key tool for learning large scale dynamical systems. Recent advances in deep neural operators have dramatically improved the accuracy and scalability of operator modeling, but lack an inherent notion of predictive uncertainty. We introduce local spectral conformal inference (LSCI), a new adaptive conformal inference procedure for black box operator models that localizes, or adapts, the spectra of the prediction sets to the spectra of the predictions. LSCI prediction sets are locally adaptive, risk controlling, and have approximate conditional coverage. We evaluate LSCI against baseline conformal methods on Navier-Stokes simulations and large weather forecasting tasks.