Adhesive bonding of metal assemblies is gaining acceptance for use with safety critical structures, and there is a need for effective inspection for both quality assurance (QA) and the assessment of condition in service. One aspect of QA is the need for the dimensions of adhesive bondlines to be within tolerance and measurable. This paper describes the application of ultrasonic Lamb waves in the determination of the principal dimensions of two forms of adhered joints (Lap and T-form) between metal plates. Low order Lamb wave modes (s0 and a1) are propagated across adhered bond-lines, and the received signals are transformed to the modulus frequency domain (FD). The FD data are used as input to artificial neural networks (ANNs), which are trained to associate features in the input data with principal bondline dimensions. The performance of different network structures and simplified forms of these is examined, and the technique gives reliable estimates of the required dimensions in bondlines not included in network training. The interconnected weights of simplified networks provide evidence of the features in Lamb wave signals that underlie the successful operation of the method.