Accurate quantification of vessel diameter in low-dose Computer Tomography (CT) images is important to study pulmonary diseases, in particular for the diagnosis of vascular diseases and the characterization of morphological vascular remodeling in Chronic Obstructive Pulmonary Disease (COPD). In this study, we objectively compare several vessel diameter estimation methods using a physical phantom. Five solid tubes of differing diameters (from 0.898 to 3.980 mm) were embedded in foam, simulating vessels in the lungs. To measure the diameters, we first extracted the vessels using either of two approaches: vessel enhancement using multi-scale Hessian matrix computation, or explicitly segmenting them using intensity threshold. We implemented six methods to quantify the diameter: three estimating diameter as a function of scale used to calculate the Hessian matrix; two calculating equivalent diameter from the crosssection area obtained by thresholding the intensity and vesselness response, respectively; and finally, estimating the diameter of the object using the Full Width Half Maximum (FWHM). We find that the accuracy of frequently used methods estimating vessel diameter from the multi-scale vesselness filter depends on the range and the number of scales used. Moreover, these methods still yield a significant error margin on the challenging estimation of the smallest diameter (on the order or below the size of the CT point spread function). Obviously, the performance of the thresholding-based methods depends on the value of the threshold. Finally, we observe that a simple adaptive thresholding approach can achieve a robust and accurate estimation of the smallest vessels diameter.