Uncovering links between processing conditions, microstructure, and properties is a central tenet of materials analysis. It is well known that microstructure determines properties, but expressing these structural features in a universal quantitative fashion has proved to be extremely difficult. Recent efforts have focused on training supervised learning algorithms to place microstructure images into predefined classes, but this approach assumes a level of a priori knowledge that may not always be available. In this paper, we expand this idea to the semi-supervised context in which class labels are known with confidence for only a fraction of the microstructures that represent the material system. It is shown that classifiers which perform well on both the high-confidence labeled data and the unlabeled, ambiguous data can be constructed by relying on the labeling consensus of a collection of semi-supervised learning methods. We also demonstrate the use of novel error estimation approaches for unlabeled data to establish robust confidence bounds on the classification performance over the entire microstructure space.