Computational time and memory for antenna optimizations rise exponentially in high-dimensional parameter spaces, as more full-wave simulations are typically required. In this work, we study the random forest algorithm in high-dimensional antenna surrogate modeling for effective reduction in computational cost. We compare this algorithm with two other popular algorithms, e.g., kriging interpolation and the support vector regression (SVR). Based on our results, the random forest algorithm shows a minimum of 9.5% improvement in surrogate modeling compared to the SVR algorithm and at least 7.72 × better performance compared to the kriging algorithm when a 20-dimensional test function problem is utilized. When a 13-dimensional antenna problem is used, our algorithm is very similar to the SVR algorithm, performing at least 2.67 × better than the kriging algorithm.