In recent years, the ability to accurately measuring and analyzing the morphology of small pulmonary structures on chest CT images, such as airways, is becoming of great interest in the scientific community. As an example, in COPD the smaller conducting airways are the primary site of increased resistance in COPD, while small changes in airway segments can identify early stages of bronchiectasis. To date, different methods have been proposed to measure airway wall thickness and airway lumen, but traditional algorithms are often limited due to resolution and artifacts in the CT image. In this work, we propose a Convolutional Neural Regressor (CNR) to perform cross-sectional measurements of airways, considering wall thickness and airway lumen at once. To train the networks, we developed a generative synthetic model of airways that we refined using a Simulated and Unsupervised Generative Adversarial Network (SimGAN). We evaluated the proposed method by first computing the relative error on a dataset of synthetic images refined with SimGAN, in comparison with other methods. Then, due to the high complexity to create an in-vivo ground-truth, we performed a validation on an airway phantom constructed to have airways of different sizes. Finally, we carried out an indirect validation analyzing the correlation between the percentage of the predicted forced expiratory volume in one second (FEV1%) and the value of the Pi10 parameter. As shown by the results, the proposed approach paves the way for the use of CNNs to precisely and accurately measure small lung airways with high accuracy.