Shallow water equations (SWE) are the main mathematical model used for predicting coastal flooding in connection with extreme events such as storm surges and tsunamis. In addition they are often applied as simulation tool for other types of coastal and regional ocean applications, including tidal, ecological, and environmental studies. Realistic coastal ocean domains often include features with predominantly one-dimensional structure such as shipping channels, rivers, narrow straits, etc. Accurately meshing and simulating in 2D such features requires very fine mesh resolution in the cross-flow direction negatively affecting the CFL condition and resulting in significant computational overhead. In this work, we introduce a coupled 1D/2D modeling approach in which our domain is divided into interacting 1D and 2D areas. Compared to already existing models, we explicitly allow our 1D domain to be embedded within the 2D domain (edges of the 2D elements) while possessing a distinct bathymetry. This increases model flexibility and improves computational efficiency by allowing for larger time steps The main difficulty lies in the numerical coupling of neighbouring 1D and 2D elements capable of preserving the mass and momentum conservation while producing no artifacts arising from interaction of 1D and 2D flows. This work uses the discontinuous Galerkin SWE solver UTBEST, which has been extended to support coupled 1D/2D domains. We demonstrate accuracy and robustness of the new model using artificial and realistic scenarios.