We introduce the notion of semantic image quality for applications where image quality relies on semantic requirements. Working in fetal ultrasound, where ranking is challenging and annotations are noisy, we design a robust coarse-to-fine model that ranks images based on their semantic image quality and endow our predicted rankings with an uncertainty estimate. To annotate rankings on training data, we design an efficient ranking annotation scheme based on the merge sort algorithm. Finally, we compare our ranking algorithm to a number of state-of-the-art ranking algorithms on a challenging fetal ultrasound quality assessment task, showing the superior performance of our method on the majority of rank correlation metrics.