The Confidence Machine is a recently developed algorithmic framework for making reliable decisions in the face of uncertainty. Control of predictive accuracy is achieved by allowing hedged predictions, with the possible sacrifice of precision. We use the Support Vector Machine learning algorithm to derive a decision rule for the classification of childhood acute leukaemia subtypes from a small training set of gene expression data. We then implement a Confidence Machine for the decision rule and test on an independent data set to demonstrate its error calibration properties. We show that the Confidence Machine can be used to derive reliable predictions, with control of the risk of error whilst maintaining the level of accuracy given by the Support Vector Machine, yielding useful and precise predictions of leukaemia subtypes. Predictions are reliable even in the context of training from small sample size.