The main purpose of this study is to compare the performance of a group of second-order designs such as Box-Behnken, face-center cube, three-level factorial, central composite, minimum bias, and minimum variance plus bias for estimating a quadratic metamodel. A time-shared computer system is used to demonstrate the ability of the designs in providing good fit of the metamodel to the simulation response. First, for various numbers of center runs, these designs are compared with respect to their efficiency, rotatability, orthogonality, robustness, bias, and prediction variance. Next, second-order metamodels are fit to the data collected using these designs. Metamodel fit is investigated using criteria such as average absolute error, PRESS, and the C-p statistic. Results indicate that the minimum variance plus bias design is the most promising design to estimate a metamodel for the case studied.