The ability to design and construct synthetic biological systems with predictable behavior could enable significant advances in medical treatment, agricultural sustainability, and bioenergy production. However, to reach a stage where such systems can be reliably designed from biological components, integrated experimental and computational techniques that enable robust component characterization are needed. In this paper we present a computational method for the automated characterization of genetic components. Our method exploits a recently developed multichannel experimental protocol and integrates bacterial growth modeling, Bayesian parameter estimation, and model selection, together with data processing steps that are amenable to automation. We implement the method within the Genetic Engineering of Cells modeling and design environment, which enables both characterization and design to be integrated within a common software framework. To demonstrate the application of the method, we quantitatively characterize a synthetic receiver device that responds to the 3-oxohexanoyl-homoserine lactone signal, across a range of experimental conditions.