  If binary intermediate-mass black holes (IMBHs; with masses between 100 and
$10^4 \Msun$) form in dense stellar clusters, their inspiral will be detectable
with the planned Laser Interferometer Space Antenna (LISA) out to several Gpc.
Here we present a study of the dynamical evolution of such binaries using a
combination of direct $N$-body techniques (when the binaries are well
separated) and three-body relativistic scattering experiments (when the
binaries are tight enough that interactions with stars occur one at a time). We
find that for reasonable IMBH masses there is only a mild effect on the
structure of the surrounding cluster even though the binary binding energy can
exceed the binding energy of the cluster. We demonstrate that, contrary to
standard assumptions, the eccentricity in the LISA band can be in {\em some}
cases as large as $\sim 0.2 - 0.3$ and that it induces a measurable phase
difference from circular binaries in the last year before merger. We also show
that, even though energy input from the binary decreases the density of the
core and slows down interactions, the total time to coalescence is short enough
(typically less than a hundred million years) that such mergers will be unique
snapshots of clustered star formation.
