This talk explores two advanced numerical methods for solving compressible two-phase flows modelled using the conservative Symmetric Hyperbolic Thermodynamically Compatible (SHTC) model proposed by Romenski et al. I first address the weak hyperbolicity of the original model in multidimensional cases by restoring strong hyperbolicity through two distinct approaches: the explicit symmetrization of the system and the hyperbolic Generalized Lagrangian Multiplier (GLM) curl-cleaning approach. Then, I will present two numerical methods to solve the proposed problem: a high-order ADER Discontinuous Galerkin (ADER-DG) scheme with an a posteriori sub-cell finite volume limiter and an exactly curl-free finite volume scheme to handle the curl involution in the relative velocity field. The latter method uses a staggered grid discretization and defines a proper compatible gradient and a curl operator to achieve a curl-free discrete solution. Extensive numerical test cases in one and multiple dimensions validate both methods' accuracy and stability.