Cerebral microbleeds (CMBs) are a recognised biomarker of traumatic axonal injury (TAI). Their number and location provide valuable information in the long-term prognosis of patients who sustained a traumatic brain injury (TBI). Accurate detection of CMBs is necessary for both research and clinical applications. CMBs appear as small hypointense lesions on susceptibility-weighted magnetic resonance imaging (SWI). Their size and shape vary markedly in cases of TBI. Manual annotation of CMBs is a difficult, error-prone, and time-consuming task. Several studies addressed the detection of CMBs in other neuropathologies with convolutional neural networks (CNNs). In this study, we developed and contrasted a classification (Patch-CNN) and two segmentation (Segmentation-CNN, U-Net) approaches for the detection of CMBs in TBI cases. The models were trained using 45 datasets, and the best models were chosen according to 16 validation sets. Finally, the models were evaluated on 10 TBI and healthy control cases, respectively. Our three models outperform the current status quo in the detection of traumatic CMBs, achieving higher sensitivity at low false positive (FP) counts. Furthermore, using a segmentation approach allows for better precision. The best model, the U-Net, achieves a detection rate of 90\% at FP counts of 17.1 in TBI patients and 3.4 in healthy controls.