When addressing water quality issues in coastal zone management, rivers are considered to be among the most significant pathways for waterborne solute transport. On the other hand, estuaries are some of the most productive environments on Earth and multiple interests from different stakeholders put additional pressure on such an ecosystem. Estuaries are thus among the most critical areas for pollution hazard and a lot of research is being conducted in order to ensure their sustainable development. The flow in an estuary is characterized by a mixing process, which results from a combination of small-scale turbulent diffusion and larger-scale variation of mean advective velocities. Scalar concentration in such turbulent flows is a random variable, which requires a statistical approach. This thesis focuses on the development of two analytical methodologies for obtaining concentration statistics of a conservative contaminant generated by a steady river flow in a salt-wedge estuary. Analytically obtained concentration statistics, which include concentration moments, probability density function defined in point, spatially integrated moments, and expected mass fraction, significantly reduce the costs and time needed for obtaining the measured data. Although these analytical models lack the level of detail possessed by sophisticated numerical models, they can generate results within seconds and with little preprocessing. Therefore, the developed analytical models represent screening tools for obtaining concentration statistics of pollution in estuaries, and can be used by stakeholders of different backgrounds. While investigating various validation procedures for the developed analytical models, and using the case study of the Žrnovnica River estuary, near Split, Croatia, several new findings were obtained. For instance, a new model for mean velocity attenuation was proposed and verified. Furthermore, a new proxy concentration was tested and, combined with numerical modeling, it delivered qualitative verification of analytically obtained concentration statistics. The analytical model for point concentration statistics was implemented in a user-friendly computer application (CPoRT) and presented to different stakeholders as a screening tool. Finally, the most important scientific contributions of this thesis are the development of the semi-analytical approach for obtaining concentration statistics in a river-dominated estuary, application of proxy concentration using the salinity data and the introduction of the expected mass fraction as a significant novelty to address the pollution loading to coastal waters.