Manual estimation of fetal Head Circumference (HC) from Ultrasound (US) is a key biometric for monitoring the healthy development of fetuses. Unfortunately, such measurements are subject to large inter-observer variability, resulting in low early-detection rates of fetal abnormalities. To address this issue, we propose a novel probabilistic Deep Learning approach for real-time automated estimation of fetal HC. This system feeds back statistics on measurement robustness to inform users how confident a deep neural network is in evaluating suitable views acquired during free-hand ultrasound examination. In real-time scenarios, this approach may be exploited to guide operators to scan planes that are as close as possible to the underlying distribution of training images, for the purpose of improving inter-operator consistency. We train on freehand ultrasound data from over 2000 subjects (2848 training/540 test) and show that our method is able to predict HC measurements within 1.81±1.65 mm deviation from the ground truth, with 50% of the test images fully contained within the predicted confidence margins, and an average of 1.82±1.78 mm deviation from the margin for the remaining cases that are not fully contained.