CT-FFR provides noninvasive estimates of Fractional Flow Reserve (FFR) from Coronary Computed Tomography Angiography (CCTA) by combining computational fluid dynamics (CFD) with vessel geometry. While deep learning has advanced medical image segmentation, even state-of-the-art methods often result in discontinuous coronary topologies in critical stenosis regions, which may lead to false diagnosis. We present a two-stage segmentation approach for extraction of CFD-viable coronary geometry based on Swin UNEt TRansformers (Swin UNETR). In the first stage, the main coronary topology was found through ensemble voting from a set of trained models. Next, a series of dilation operations was performed to generate a region of interest (ROI) around the coronary arteries. The final segmentation was predicted by a Swin UNETR model where the ROI was provided as an input. The two-stage ROI-approach was compared with a baseline/single Swin UNETR model for a set of 15 CCTAs with ground truth segmentations performed by two independent operators. The average DICE score for the single Swin UNETR approach was 0.891, which was improved to 0.912 by the two-stage approach. In comparison, the interobserver DICE score was 0.906. The automatic segmentations were integrated in a CT-FFR pipeline to facilitate automatic prediction of FFR. CT-FFR predictions corresponding to the two-stage approach achieved better agreement with invasive FFR (r: 0.77, std. error: 0.089) compared to predictions based on manual segmentations (r: 0.63, std. error: 0.123 for operator 1 and, r: 0.47, std. error: 0.119 for operator 2). In contrast, the segmentations based on the baseline Swin UNETR resulted in disconnected segments in critical stenosis regions and poor CT-FFR agreement (r: 0.14, std.error: 0.180).