With growing interest in the model-based realization of engineered systems there is a need for developing methods to explore the solution space that is defined by models that approximate reality and are typically incomplete, inaccurate with different fidelities. These characteristics of model-based engineered systems manifest as uncertainties in the projected outcomes and it requires good understanding, insight and analysis of the designs/solutions in order to support the designer in the process of decision making. Therefore, a significant and desirable step in any model-based realization of engineered systems is to explore the solution space and find desired and robust designs insensitive to variations of different sources. In this thesis a method is proposed to conduct solution space exploration in model-based realization of engineered systems. The construct that is adapted to develop the models is the compromise Decision Support Problem (cDSP). The solutions that form the solution space in the compromise DSP comprises the space defined by the constraints and variable bounds, and the achieved and aspiration space defined by the goals. The main components of the proposed method are: exploring design goals through goal ordering and weight sensitivity analysis, exploring constraints through constraint sensitivity analysis, and incorporating feasibility robustness. The proposed method in this thesis is illustrated in three different design examples namely a small power plant, shell and tube heat exchanger and continuous casting of steel. The emphasis is on the method rather than the results per se. To generalize the method, the post solution analysis template is proposed to facilitate executability and reusability of the solution space exploration method in a computer.