Abstract To progress in the characterization of noise for quantum computers, gate set tomography (GST) has emerged as a self-consistent protocol that accurately estimates noisy gates, state preparations, and measurements. In its original incarnation, GST improves estimation precision by applying gates sequentially, assuming the noise yields fixed completely-positive and trace-preserving (CPTP) maps independent of prior gate history. This ‘Markovian’ assumption can conflict with experiments, where time-correlated noise may induce non-Markovian dynamics, or slow drifts and cumulative calibration errors introduce context dependence, causing CP-divisible maps to vary with circuit depth. In this work, we address this issue for trapped-ion devices with phonon-mediated two-qubit gates. Using detailed microscopic modeling of high-fidelity light-shift gates, we tailor GST to capture the main source of context dependence: motional degrees of freedom. Rather than invalidating GST, context dependence can be incorporated into the gate-set parametrization, reducing sampling cost. Our results identify a promising research avenue that might be applicable to other platforms where microscopic modeling can be incorporated: the development of a context-aware GST. Similar content being viewed by others Acknowledgements The project leading to this publication has received funding from the US Army Research Office through Grant No. W911NF-21-1-0007. We acknowledge support from PID2021-127726NB-I00 (MCIU/AEI/FEDER, UE), from the Grant IFT Centro de Excelencia Severo Ochoa CEX2020-001007-S, funded by MCIN/AEI/10.13039/501100011033, from the CSIC Research Platform on Quantum Technologies PTI-001, and from the European Union’s Horizon Europe research and innovation program under grant agreement No 101114305 ("MILLENION-SGA1” EU Project). Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the granting authority can be held responsible for them. Author information Authors and Affiliations Corresponding author Ethics declarations Competing interests The authors declare no competing interests. Additional information