Facial landmark detection plays an important role for the similarity analysis in artworks to compare portraits of the same or similar artists. With facial landmarks, portraits of different genres, such as paintings and prints, can be automatically aligned using control-point-based image registration. We propose a deep-learning-based method for facial landmark detection in high-resolution images of paintings and prints. It divides the task into a global network for coarse landmark prediction and multiple region networks for precise landmark refinement in regions of the eyes, nose, and mouth that are automatically determined based on the predicted global landmark coordinates. We created a synthetically augmented facial landmark art dataset including artistic style transfer and geometric landmark shifts. Our method demonstrates an accurate detection of the inner facial landmarks for our high-resolution dataset of artworks while being comparable for a public low-resolution artwork dataset in comparison to competing methods.