Vortices may occur inside the coating bead flow of the slot die coating process under specific operating conditions. Once formed, they may cause various issues, such as particle aggregation and destruction of widthwise flow uniformity, which significantly hinder the operation of the coating process and decrease the quality of the final product. Therefore, it is essential to identify in advance the range of operating conditions that result in vortex formation and prevent operating within that range. If the vortex formation is inevitable with the operating conditions under consideration, it is also important to quantify the vortex flow in order to assess the relative 'safety' of each set of operating conditions. This study presents a systematic method for identifying and quantifying the vortex formation in the coating bead flow. First, the velocity and pressure profiles of the coating flow under predefined sets of operating conditions. Since it is infeasible to directly explore the high-dimensional parametric space, parameters associated with vortex formation (e.g. substrate speed, coating gap, fluid viscosity) were grouped into dimensionless groups, and the case studies were carried out in the space of those groups. Galerkin finite element method (G/FEM) was used to obtain the unknown velocity and pressure fields given the set of dimensionless operating parameters. The case study was aided by the multiparameter continuation that consists of a predictor step where a 'good' initial guess is generated given the step change in the continuation parameter and a corrector step where the new solution is obtained using the initial guess. Stream function values are computed numerically from the obtained velocity field, and level sets of the stream function are examined in search of those that form a closed loop. The obtained closed loops are then clustered in terms of their center coordinates. The loops with the maximum area in each cluster are then identified as the boundaries of the vortices. By using this method, it was possible to obtain the mapping from dimensionless operating parameters to the area of vortices and evaluate the effect of each parameter on the vortex formation in the coating bead flow.