Although the recent development of solar power forecasting through machine learning approaches, such as the machine learning models based on numerical weather prediction (NWP) data, has been remarkable, their extreme error requires an increase in the amount of reserve capacity procurement used for the power system safety. Hence, a reduction of the serious overestimation is necessary for efficient grid operation. However, despite the importance of the above issue, few studies have focused on the model design, suppressing serious errors, to the best of the authors’ knowledge. This study investigates a prediction model that can reduce the huge overestimation of the solar irradiance, which poses a risk to the power system. The specific approaches used are as follows: the employment of Support Vector Quantile Regression (SVQR), the utilization of Meso-scale Ensemble Prediction System (MEPS, Meso-scale EPS for the regions of Japan) data, which is based on the forecasts from Meso-scale Model (MSM) as explanatory variables, and the hyperparameter adjustment. The performance of the models is verified in the one day-ahead forecasting for surface solar irradiance at five sites in the Kanto region as the numerical simulation, where their forecasting errors are measured by the root mean square error (RMSE) and the 3σ error, which corresponds to the 99.87% quantile error of the order statistics. The test results indicate the following findings: the SVRs’ RMSE and 3σ error tend to be trade-offs in the case of varying the penalty of the regularization term; by using SVR as a post-processing tool for MSM or MEPS data, both of the score of their metrics can be improved from original data; the MEPS-based SVQR (MEPS-SVQR) could provide superior performance in both metrics in comparison with the MSM-based SVQR (MSM-SVQR) if the parameters are properly adjusted. Although the time period and the type of MEPS data used for the validation are limited, our report is expected to help the design of NWP-based machine learning models to enable short-term solar power forecasts with a low risk of overestimation.