Recent proliferation of powerful AI systems has created a strong need for capabilities that help users to calibrate trust in those systems. As AI systems grow in scale, information required to evaluate their trustworthiness becomes less accessible, presenting a growing risk of using these systems inappropriately. We propose the Trust Calibration Maturity Model (TCMM) to characterize and communicate information about AI system trustworthiness. The TCMM incorporates five dimensions of analytic maturity: Performance Characterization, Bias & Robustness Quantification, Transparency, Safety & Security, and Usability. The TCMM can be presented along with system performance information to (1) help a user to appropriately calibrate trust, (2) establish requirements and track progress, and (3) identify research needs. Here, we discuss the TCMM and demonstrate it on two target tasks: using ChatGPT for high consequence nuclear science determinations, and using PhaseNet (an ensemble of seismic models) for categorizing sources of seismic events.