Abstract We use perfect‐model, large‐ensemble nonlinear Recharge Oscillator (RO) simulations to quantify ENSO internal variability and the detectability of forced changes in ENSO characteristics. Fixed‐parameter simulations show that linear trends in ENSO standard deviation, period, and skewness as large as those observed since 1955 can arise from internal variability in 10% of simulations. RO parameters estimated from single realizations exhibit spurious drifts even without forcing, underscoring the need for ensembles. Using 100‐member ensembles, comparable to the largest climate‐model ensembles, we identify detectable parameter trends. For ENSO amplitude, detectability thresholds for forced changes in underlying processes are 15% per century for stochastic forcing, 25% per century for basin adjustment, and 50% per century for the Bjerknes feedback. For ENSO period, the detectability threshold for forced changes in the underlying recharge–discharge processes and delayed oceanic feedback is 15% per century. These results provide a testbed for interpreting RO‐diagnosed ENSO changes in climate‐model ensembles.