  Supermassive black hole binaries (SMBHBs) with masses in the range 10^4-10^7
M_sun/(1+z), produced in galaxy mergers, are thought to complete their
coalescence due to the emission of gravitational waves (GWs). The anticipated
detection of the GWs by the LISA will constitute a milestone for fundamental
physics and astrophysics. While the GW signatures themselves will provide a
treasure trove of information, if the source can be securely identified in
electromagnetic (EM) bands, this would open up entirely new scientific
opportunities, to probe fundamental physics, astrophysics, and cosmology. We
discuss several ideas, involving wide-field telescopes, that may be useful in
locating electromagnetic counterparts to SMBHBs detected by LISA. In
particular, the binary may produce a variable electromagnetic flux, such as a
roughly periodic signal due to the orbital motion prior to coalescence, or a
prompt transient signal caused by shocks in the circumbinary disk when the
SMBHB recoils and "shakes" the disk. We discuss whether these time-variable EM
signatures may be detectable, and how they can help in identifying a unique
counterpart within the localization errors provided by LISA. We also discuss a
possibility of identifying a population of coalescing SMBHBs statistically, in
a deep optical survey for periodically variable sources, before LISA detects
the GWs directly. The discovery of such sources would confirm that gas is
present in the vicinity and is being perturbed by the SMBHB - serving as a
proof of concept for eventually finding actual LISA counterparts.
