Tissue microarrays (TMAs) facilitate the survey of very large numbers of tumours. However, the manual assessment of stained TMA sections constitutes a bottleneck in the pathologist's work-flow. This paper presents a computational pipeline for automatically classifying and scoring breast cancer TMA spots that have been subjected to nuclear immunostaining. Spots are classified based on a bag of visual words approach. Immunohistochemical scoring is performed by computing spot features reflecting the proportion of epithelial nuclei that are stained and the strength of that staining. These are then mapped onto an ordinal scale used by pathologists. Multi-layer perceptron classifiers are compared with Latent topic models and support vector machines for spot classification, and with Gaussian process ordinal regression and linear models for scoring. Intra-observer variation is also reported. The use of posterior entropy to identify uncertain cases is demonstrated. Evaluation is performed using TMA images stained for progesterone receptor.