The current trend towards miniaturization of modern consumer electronic devices significantly affects their design. The demand for efficient all-in-one appliances leads to smaller, yet more complex and powerful nanoelectronic devices. The increasing complexity in the design of such nanoscale Analog/Mixed-Signal Systems-on-Chip (AMS-SoCs) presents difficult challenges to designers. One promising design method used to mitigate the burden of this design effort is the use of metamodeling (surrogate) modeling techniques. Their use significantly reduces the time for computer simulation and design space exploration and optimization. This dissertation addresses several issues of metamodeling based nanoelectronic based AMS design exploration. A surrogate modeling technique which uses geostatistical based Kriging prediction methods in creating metamodels is proposed. Kriging prediction techniques take into account the correlation effects between input parameters for performance point prediction. We propose the use of Kriging to utilize this property for the accurate modeling of process variation effects of designs in the deep nanometer region. Different Kriging methods have been explored for this work such as simple and ordinary Kriging. We also propose another metamodeling technique Kriging-Bootstrapped Neural Network that combines the accuracy and process variation awareness of Kriging with artificial neural network models for ultra-fast and accurate process aware metamodeling design. The proposed methodologies combine Kriging metamodels with selected algorithms for ultra-fast layout optimization. The selected algorithms explored are: Gravitational Search Algorithm (GSA), Simulated Annealing Optimization (SAO), and Ant Colony Optimization (ACO). Experimental results demonstrate that the proposed Kriging metamodel based methodologies can perform the optimizations with minimal computational burden compared to traditional (SPICE-based) design flows.