Shared decision-making (SDM) is necessary to achieve patient-centred care. Currently no methodology exists to automatically measure SDM at scale. This study aimed to develop an automated approach to measure SDM by using language modelling and the conversational alignment (CA) score. A total of 157 video-recorded patient-doctor conversations from a randomized multi-centre trial evaluating SDM decision aids for anticoagulation in atrial fibrillations were transcribed and segmented into 42,559 sentences. Context-response pairs and negative sampling were employed to train deep learning (DL) models and fine-tuned BERT models via the next sentence prediction (NSP) task. Each top-performing model was used to calculate four types of CA scores. A random-effects analysis by clinician, adjusting for age, sex, race, and trial arm, assessed the association between CA scores and SDM outcomes: the Decisional Conflict Scale (DCS) and the Observing Patient Involvement in Decision-Making 12 (OPTION12) scores. p-values were corrected for multiple comparisons with the Benjamini-Hochberg method. Among 157 patients (34% female, mean age 70 SD 10.8), clinicians on average spoke more words than patients (1911 vs 773). The DL model without the stylebook strategy achieved a recall@1 of 0.227, while the fine-tuned BERTbase (110M) achieved the highest recall@1 with 0.640. The AbsMax (18.36 SE7.74 p=0.025) and Max CA (21.02 SE7.63 p=0.012) scores generated with the DL without stylebook were associated with OPTION12. The Max CA score generated with the fine-tuned BERTbase (110M) was associated with the DCS score (-27.61 SE12.63 p=0.037). BERT model sizes did not have an impact the association between CA scores and SDM. This study introduces an automated, scalable methodology to measure SDM in patient-doctor conversations through explainable CA scores, with potential to evaluate SDM strategies at scale.