This article describes how artificial neural networks (ANNs) can be used to benefit a number of RF and microwave measurement areas including vector network analysis (VNA). We apply ANNs to model a variety of on-wafer and coaxial VNA calibrations, including open-short-load-thru (OSLT) and line-reflect-match (LRM), and assess the accuracy of the calibrations using these ANN-modeled standards. We find that the ANN models compare favorably to benchmark calibrations throughout the frequencies they were trained for. We summarize other current applications of ANNs, including the determination of permittivities of liquids from the reflection coefficient measurements of an open-ended coaxial probe and the determination of moisture content of wheat from free-space transmission coefficient measurements. We also discuss some potential applications of ANN models related to power measurements, material characterization, and the comparison of nonlinear vector network analyzers.