The control of beam phase relative to the accelerating RF field within a superconducting cavity is important in many accelerator applications and is of particular importance for a free electron laser facility. As standard practice, the phase is usually inferred from the beam-induced transient field with respect to a timing reference. We report here on an alternative and novel means of beam phase determination based on beam-excited higher order electromagnetic modes and the accelerating electromagnetic mode, which are conveniently available from the same coupler. The monopole modes are immune to the electron beam offset and therefore are best suited for the task. A coupled circuit model is used to assist the development and to rapidly assess the facility of the method. Simulations based on the circuit model indicate that the resolution of this system depends critically on the signal to noise ratio. Beam-based measurements with a test setup were carried out at the European XFEL, Germany. Based on this new method we have routinely obtained a resolution of 0.1°. The best resolution observed with the current setup was 0.03°. These results agree very well with the predictions from those predicted by a circuit model. The system investigated here can be used to provide diagnostic information for the current LLRF system employed in the European XFEL. To this end, the associated electronics are under development. This monitor is the first of its kind that can deliver direct and online measurements of the beam phase with respect to the RF field.