While most calibration methods focus on inferring a set of model parameters that are unknown but assumed to be constant, many models have parameters that have a functional relation with the controllable input variables. Formulating a low-dimensional approximation of these calibration functions allows modelers to use low-fidelity models to explore phenomena at lengths and time scales unattainable with their high-fidelity sources. While functional calibration methods are available for low-dimensional problems (e.g., one to three unknown calibration functions), exploring high-dimensional spaces of unknown calibration functions (e.g., more than ten) is still a challenging task due to its computational cost and the risk for identifiability issues. To address this challenge, we introduce a semiparametric calibration method that uses an approximate Bayesian computation scheme to quantify the uncertainty in the unknown calibration functions and uses this insight to identify what functions can be replaced with low-dimensional approximations. Through a test problem and a coarse-grained model of an epoxy resin, we demonstrate that the introduced method enables the identification of a low-dimensional set of calibration functions with a limited compromise in calibration accuracy. The novelty of the presented method is the ability to synthesize domain knowledge from various sources (i.e., physical experiments, simulation models, and expert insight) to enable high-dimensional functional calibration without the need for prior knowledge on the class of unknown calibration functions.