The parameter estimation problem for the coupled ocean–atmosphere system in the tropical Pacific Ocean is investigated using an advanced sequential estimator [i.e., the extended Kalman filter (EKF)]. The intermediate coupled model (ICM) used in this paper consists of a prognostic upper-ocean model and a diagnostic atmospheric model. Model errors arise from the uncertainty in atmospheric wind stress. First, the state and parameters are estimated in an identical-twin framework, based on incomplete and inaccurate observations of the model state. Two parameters are estimated by including them into an augmented state vector. Model-generated oceanic datasets are assimilated to produce a time-continuous, dynamically consistent description of the model’s El Niño–Southern Oscillation (ENSO). State estimation without correcting erroneous parameter values still permits recovering the true state to a certain extent, depending on the quality and accuracy of the observations and the size of the discrepancy in the parameters. Estimating both state and parameter values simultaneously, though, produces much better results. Next, real sea surface temperatures observations from the tropical Pacific are assimilated for a 30-yr period (1975–2004). Estimating both the state and parameters by the EKF method helps to track the observations better, even when the ICM is not capable of simulating all the details of the observed state. Furthermore, unobserved ocean variables, such as zonal currents, are improved when model parameters are estimated. A key advantage of using this augmented-state approach is that the incremental cost of applying the EKF to joint state and parameter estimation is small relative to the cost of state estimation alone. A similar approach generalizes various reduced-state approximations of the EKF and could improve simulations and forecasts using large, realistic models.