When two galaxies merge, their SMBHs form a binary system at the center of the merged system, which eventually coalescences due to the energy lost in the form of gravitational waves. General Relativity predicts that the gravitational wave emission is strongly anisotropic for certain orbital configurations, which causes the merged SMBH to recoil with a large velocity, up to several 1000 km/s. The recoiling SMBH subsequently undergoes long-lived (~1 Gyr) oscillations in the host galaxy and while it is actively accreting, it can be observed as an AGN that is offset from the center of its galaxy. The predicted offset AGN provide electromagnetic “signposts” of binary SMBH coalescence events, which although they are extremely luminous gravitational wave sources, cannot be detected by current gravitational wave detectors. We are searching for gravitationally recoiling SMBH both by measuring spatial displacements between the AGN and the center of its host galaxy and by measuring doppler shifts between the AGN emission lines and the host galaxy. In an analysis of Hubble Space Telescope images of a large sample of active elliptical galaxies, we have identified about a dozen cases in which the AGN is displaced, possibly as a result of residual gravitational recoil oscillations. In addition, we previously identified the quasar E1821+643 as a recoil candidate from doppler shifts in its polarized light. To confirm this, we are looking for the expected spatial offset using a combination of spectroastrometry and HST images.