Experimentation and approximation are essential for efficiency and effectiveness in concurrent engineering analyses of large-scale complex systems. The approximation-based design strategy is not fully utilized in industrial applications in which designers have to deal with multi-disciplinary, multi-variable, multi-response, and multi-objective analysis using very complicated and expensive-to-run computer analysis codes or physical experiments. With current experimental design and metamodeling techniques, it is difficult for engineers to develop acceptable metamodels for irregular responses and achieve good design solutions in large design spaces at low prices. To circumvent this problem, engineers tend to either adopt low-fidelity simulations or models with which important response properties may be lost, or restrict the study to very small design spaces. Information from expensive physical or computer experiments is often used as a validation in late design stages instead of analysis tools that are used in early-stage design. This increases the possibility of expensive re-design processes and the time-to-market. In this dissertation, two methods, the Sequential Exploratory Experimental Design (SEED) and the Efficient Robust Concept Exploration Method (E-RCEM) are developed to address these problems. The SEED and E-RCEM methods help develop acceptable metamodels for irregular responses with expensive experiments and achieve satisficing design solutions in large design spaces with limited computational or monetary resources. It is verified that more accurate metamodels are developed and better design solutions are achieved with SEED and E-RCEM than with traditional approximation-based design methods. SEED and E-RCEM facilitate the full utility of the simulation-and-approximation-based design strategy in engineering and scientific applications. Several preliminary approaches for metamodel validation with additional validation points are proposed in this dissertation, after verifying that the most-widely-used method of leave-one-out cross-validation is theoretically inappropriate in testing the accuracy of metamodels. A comparison of the performance of kriging and MARS metamodels is done in this dissertation. Then a sequential metamodeling approach is proposed to utilize different types of metamodels along the design timeline. Several single-variable or two-variable examples and two engineering example, the design of pressure vessels and the design of unit cells for linear cellular alloys, are used in this dissertation to facilitate our studies.