Environmental pollution and fossil fuel depletion have prompted the need for renewable energy-based power generation. However, its stability is often challenged by low energy density and non-stationary conditions. Wave energy converters (WECs), in particular, need reliable real-time wave height prediction to address these issues caused by irregular wave patterns, which can lead to the inefficient and unstable operation of WECs. In this study, we propose an AI-powered reliable real-time wave height prediction model that integrates long short-term memory (LSTM) networks for temporal prediction with deep ensemble (DE) for robust uncertainty quantification (UQ), ensuring high accuracy and reliability. To further enhance the reliability, uncertainty calibration is applied, which has proven to significantly improve the quality of the quantified uncertainty. Using real operational data from an oscillating water column-wave energy converter (OWC-WEC) system in Jeju, South Korea, the model achieves notable accuracy (R2 > 0.9), while increasing uncertainty quality by over 50% through simple calibration technique. Furthermore, a comprehensive parametric study is conducted to explore the effects of key model hyperparameters, offering valuable guidelines for diverse operational scenarios, characterized by differences in wavelength, amplitude, and period. These results demonstrate the model's capability to deliver reliable predictions, facilitating digital twin of the ocean.