Over the past several years a number of high-resolution studies conducted with Earth-based and spaceborne very long baseline interferometry systems provided a large volume of experimental data on the phenomenon of supermassive black hole binaries. These objects manifest themselves as active galactic nuclei, observable in all domains of the electromagnetic spectrum. At the same time, these objects are responsible for generating gravitational waves with predictable parameters. Synergistic studies of their electromagnetic and gravitational wave emission constitute the essence of modern multimessenger astrophysics and offer hitherto unavailable opportunities for addressing fundamental questions of physics and cosmology. As a study case we present recent results of high-resolution monitoring of the quasar J2102+6015. This object demonstrates quasi-periodic astrometric oscillations which might be indicative of the presence of SMBHB in its nuclei. We analyse parameters of this nuclei and consider various scenarios of its astrophysical evolution which involves gravitational wave emission as an important ingredient. This analysis might serve as an input into evaluation of specifications for future gravitational wave telescopes able to operate in the sub-millihertz domain of gravitational wave spectrum. In this presentation we emphasise the case for joint investigations of SMBHB by VLBI and gravitational wave telescopes as unique and potentially transformational means of understanding fundamental properties of gravitation. Since SMBHB are observable at a broad range of redshifts, the combination of high-resolution VLBI and gravitational wave studies would offer powerful tool for decisive cosmological tests. Especial role in these tests would be performed by next generation space VLBI missions at millimeter and submillimeter wavelengths prototyped in the TeraHertz Exploration and Zooming-in for Astrophysics concept developed in the framework of the ESA's Voyage 2050 programme.
