In this paper we propose multi-output kernel ridge regression (KRR) for out-of-sample mapping in supervised manifold learning, in place of general regression neural networks (GRNN) that have been adopted by previous studies on the subject. Specifically, we consider a supervised agglomerative variant of Isomap and compare the performance of classification methods when the out-of-sample embedding is based on KRR and GRNN, respectively. Extensive computational experiments, using support vector machines and k-nearest neighbors as base classifiers, provide statistical evidence that out-of-sample mapping based on KRR consistently dominates its GRNN counterpart, and that supervised agglomerative Isomap with KRR achieves a higher accuracy than direct classification methods on most data sets.