  This paper studies the formation and evolution of binary supermassive black
holes (SMBHs) in rotating galactic nuclei, focusing on the role of stellar
dynamics. We present the first N-body simulations that follow the evolution of
the SMBHs from kiloparsec separations all the way to their final relativistic
coalescence, and that can robustly be scaled to real galaxies. The N-body code
includes post-Newtonian (PN) corrections to the binary equations of motion up
to order 2.5; we show that the evolution of the massive binary is only
correctly reproduced if the conservative 1PN and 2PN terms are included. The
orbital eccentricities of the massive binaries in our simulations are often
found to remain large until shortly before coalescence. This directly affects
not only their orbital evolution rates, but has important consequences as well
for the gravitational waveforms emitted during the relativistic inspiral. We
estimate gravitational wave amplitudes when the frequencies fall inside the
band of the (planned) Laser Interferometer Space Antennae (LISA). We find
significant contributions -- well above the LISA sensitivity curve -- from the
higher-order harmonics.
