Regarding the high significance of correct pan evaporation modeling, this study introduces two novel neuro-metaheuristic approaches to improve the accuracy of prediction for this parameter. Vortex search algorithms (VSA), sunflower optimization (SFO), and stochastic fractal search (SFS) are integrated with a multilayer perceptron neural network to create the VSA-MLPNN, SFO-MLPNN, and SFS-MLPNN hybrids. The climate data of Arcata-Eureka station (operated by the US environmental protection agency) belonging to the years 1986-1989 and the year 1990 are used for training and testing the models, respectively. Trying different configurations revealed that the best performance of the VSA, SFO, and SFS is obtained for the population size of 400, 300, and 100, respectively. The results were compared with a conventionally trained MLPNN to examine the effect of the metaheuristic algorithms. Overall, all four models presented a very reliable simulation. However, the SFS-MLPNN (mean absolute error, MAE = 0.0997 and Pearson correlation coefficient, RP = 0.9957) was the most accurate model, followed by the VSA-MLPNN (MAE = 0.1058 and RP = 0.9945), conventional MLPNN (MAE = 0.1062 and RP = 0.9944), and SFO-MLPNN (MAE = 0.1305 and RP = 0.9914). The findings indicated that employing the VSA and SFS results in improving the accuracy of the neural network in the prediction of pan evaporation. Hence, the suggested models are recommended for future practical applications.