The precision of a measurement system is the consistency across multiple measurements of the same object. This paper studies the evaluation of the precision of measurement systems that measure on a bounded ordinal scale. A bounded ordinal scale consists of a finite number of categories that have a specific order. Based on an inventory of methods for the evaluation of precision for other types of measurement scales, the article proposes two approaches. The first approach is based on a latent variable model and is a variant of the intraclass correlation method. The second approach is a non-parametric approach, the results of which are, however, rather difficult to interpret. The approaches are illustrated with an artificial data set and an industrial data set.