This work proposes a new system capable of real-time ship instance segmentation during maritime surveillance missions by unmanned aerial vehicles using an onboard standard RGB camera. The implementation requires two stages: an instance segmentation network able to produce fast and reliable preliminary segmentation results and a post-processing 3D fully connected Conditional Random Field, which significantly improves segmentation results by exploring temporal correlations between nearby frames in video sequences. Moreover, due to the absence of maritime datasets consisting of properly labeled video sequences, we create a new dataset comprising synthetic video sequences of maritime surveillance scenarios (MarSyn). The main advantages of this approach are the possibility of generating a vast set of images and videos, being able to represent real-world scenarios without the necessity of deploying the real vehicle, and automatic labels, which eliminate human labeling errors. We train the system with the MarSyn dataset and with aerial footage from publicly available annotated maritime datasets to validate the proposed approach. We present some experimental results and compare them to other approaches, and we also illustrate the temporal stability provided by the second stage in missing frames and wrong segmentation scenarios.