Aerospace and communication engineering technologies are in constant need of microwaves with extremely high spectral purity and stability. Unfortunately, the generation of such ultra-pure microwaves with compact, versatile and transportable sources is still a very complex challenge. In aerospace engineering, ultra-stable quartz oscillators are overwhelmingly dominant as key components for both navigation and detection systems. However, it is unanimously recognized today that their frequency stability performance is reaching its floor, and will not improve significantly anymore. In the search for an alternative standard for the next generation of ultra-pure microwave sources in aerospace technology, we propose the exploration of an elegant and promising solution relying on optical resonators with ultra-high Q factors (Q ~ 1E10). In these quasi-perfectly shaped cavities, nonlinear effects are significantly enhanced and microwave generation is performed through the extraction of the intermodal frequency. This approach has several advantages over existing or other prospective methods: conceptual simplicity, higher robustness, smaller power consumption, longer lifetime, immunity to interferences, very compact volume, frequency versatility, easy chip integration, as well as a strong potential for integrating the mainstream of standard photonic components for both microwave and lightwave technologies. Our ambition in the NextPhase project is to significantly outperform quartz oscillators and demonstrate performances comparable to cryogenic sapphire oscillators, with a compact (< 100 cm3), versatile (up to at least 200 GHz) and ultra-stable (Allan variance ~ 1E-15 at 1 s; phase noise floor < -160 dBc/Hz) microwave photonic generator. We also expect our work to open new opportunities of research in optical communications (photonic components for full-optical processing, carrier synthesis), as well as in fundamental aspects of condensed matter and quantum physics.