In recent years, many dispersive models extending the shallow water equations have been derived in order to also model waves in the deep sea with smaller wavelengths. We use the general framework of summation by parts operators to construct conservative, entropy-stable and well-balanced semidiscretizations of two different nonlinear systems of dispersive shallow water equations with varying bathymetry: A variant of the coupled Benjamin-Bona-Mahony (BBM) equations [1] and a recently proposed model by Svärd and Kalisch [3] with enhanced dispersive behavior. Both models share the property of being conservative in terms of a nonlinear invariant. This property is preserved exactly in our novel semidiscretizations. Using summation by parts operators, the numerical scheme can be formulated as finite difference, continuous Galerkin and discontinuous Galerkin method of arbitrary order. In addition, we present and analyze upwind discretizations. To obtain fully-discrete entropy-stable schemes, we employ the relaxation method [2]. We present the improved numerical properties of our schemes in various test cases including a comparison with experimental data. References [1] S. Israwi, H. Kalisch, T. Katsaounis, and D. Mitsotakis. “A regularized shallow-water waves system with slip-wall boundary conditions in a basin: theory and numerical analysis”. In: Nonlinearity 35.1 (2021), pp. 750–786. doi: 10 . 1088 / 1361 - 6544 / ac3c29. [2] D. I. Ketcheson. “Relaxation Runge-Kutta Methods: Conservation and Stability for Inner-Product Norms”. In: SIAM Journal on Numerical Analysis 57.6 (2019), pp. 2850–2870. doi: 10.1137/19M1263662. [3] M. Svärd and H. Kalisch. A novel energy-bounded Boussinesq model and a well bal- anced and stable numerical discretisation. 2023. arXiv: 2302.09924 [math.NA].