qMT has been suggested as a biomarker in Glioblastoma patients. However, reconstruction involves a computationally expensive fitting procedure involving the Bloch-McConnell equations. In this work, the use of neural networks was investigated to perform the fit and to compute uncertainty heatmaps to identify regions of potential error. The dataset consisted of 164 scans from N=41 glioblastoma patients (33=training, 8=testing). Models were evaluated using MAE and correlation in the whole-head volumes and specific ROIs. The model output agreed with a conventional curve-fitting algorithm (r=0.93, and <1% error) with speed up factors of 240000x. Uncertainty predictions were correlated with prediction error (r=0.59).