Calibration is performed in eye-tracking studies to map raw model outputs to gaze-points on the screen and improve accuracy of gaze predictions. Calibration parameters, such as user-screen distance, camera intrinsic properties, and position of the screen with respect to the camera can be easily calculated in controlled offline setups, however, their estimation is non-trivial in unrestricted, online, experimental settings. Here, we propose the application of deep learning models for eye-tracking in online experiments, providing suitable strategies to estimate calibration parameters and perform personal gaze calibration. Focusing on fixation accuracy, we compare results with respect to calibration frequency, the time point of calibration during data collection (beginning, middle, end), and calibration procedure (fixation-point or smooth pursuit-based). Calibration using fixation and smooth pursuit tasks, pooled over three collection time-points, resulted in the best fixation accuracy. By combining device calibration, gaze calibration, and the best-performing deep-learning model, we achieve an accuracy of 2.580−a considerable improvement over reported accuracies in previous online eye-tracking studies.