Due to conservative design models and safe construction practices, civil-infrastructure elements, such as bridges, usually have unknown amounts of reserve capacity that exceed code requirements. The quantification of this reserve capacity may lead to better asset management by avoiding unnecessary replacement. However, this task is challenging due to high uncertainty levels that are present in structural-behavior models. These uncertainties can be reduced using field measurements associated with structural-identification methodologies. To maximize the information from monitoring, the choice of the measurement system is crucial and can be seen as an optimization task. Although an optimal measurement system must present several characteristics, only the information-gain criterion is usually taken into account. This study presents a framework to design measurement systems using multiple-objective functions. The Exeter Bascule Bridge (UK) is used as case study and the recommended measurement systems are proposed for multiple settings of asset-manager preferences. The framework supports a rational selection of measurement systems between close alternatives.