Electromagnetic (EM) simulators are regarded as highly accurate to predict the behavior of microwave circuits. With the increasing availability of commercial EM field solvers, it is very desirable to include them in the statistical analysis and yield-driven design of high speed circuits. Given the high cost in computational effort imposed by EM simulators, smart procedures must be searched to efficiently use them for statistical analysis and design. Artificial Neural Networks (ANN) and Space Mapping (SM) have been efficiently combined to formulate EM-based design algorithms. We describe in this work the use of neural space mapping methods for efficient and accurate EM-based statistical analysis and yield optimization of high frequency electronic structures. We formulate the yield optimization problem using SMbased neuromodels, which can be obtained either from a modeling process or from a design process. The SM-based neuromodel combines the computational efficiency of coarse models (typically equivalent circuit models) with the accuracy of fine models (typically EM simulators). The statistical analysis and design is realized in the frequency domain. A general equation to express the relationship between the fine and coarse model sensitivities through a nonlinear, frequency-sensitive neuromapping is reviewed. We describe the use of SM-based neuromodels for symmetric and asymmetric variations in the tolerances of the physical design parameters. We illustrate our technique by the yield analysis and optimization of a high-temperature superconducting (HTS) quarter-wave parallel coupledline microstrip filter.