An insight into the operation of molecular motors has already been obtained under in vitro conditions from single-molecule tracking of proteins. It remains to analyse the effects of these motors on the position and secretion of specific organelles in the environment of the cell. For this purpose, we have investigated the accuracy of a standard algorithm to enable the tracking of particles in live-cell microscopy. The results have been applied to an example study into the role of the microtubule-motor kinesin on the function of COPII-coated secretory-cargo exit sites forming part of the mammalian endoplasmic reticulum. These exit sites are marked with multiple EYFP-tagged proteins to produce bright fluorescent particles, and a demonstration of the motility of vesicles, under different conditions in the cell, is described here. It is essential to use a low-level expression of fluorescent protein-tagged cellular components to ensure faithful replication for the behaviour of endogenous protein. However, this leads to a lower ratio for the signal-to-noise than is desired for the sub-pixel tracking of objects in digital images. This has driven the present effort to develop a computational model of the experiment in order to estimate the precision for localization of a fluorescent particle. Our work gives a greater insight, than has been managed in the past, into the accuracy and precision of particle tracking from live-cell imaging under a variety of different conditions, and it takes into consideration the current standards in digital technology for optical microscopy.