  Using broadband ferromagnetic resonance, we measure the damping parameter of
[Co(5 \r{A})/Pt(3 \r{A})]${\times 6}$ multilayers whose growth was optimized to
maximize the perpendicular anisotropy. Structural characterizations indicate
abrupt interfaces essentially free of intermixing despite the miscible
character of Co and Pt. Gilbert damping parameters as low as 0.021 can be
obtained despite a magneto-crystalline anisotropy as large as
$10^6~\textrm{J/m}^3$. The inhomogeneous broadening accounts for part of the
ferromagnetic resonance linewidth, indicating some structural disorder leading
to a equivalent 20 mT of inhomogenity of the effective field. The unexpectedly
relatively low damping factor indicates that the presence of the Pt heavy metal
within the multilayer may not be detrimental to the damping provided that
intermixing is avoided at the Co/Pt interfaces.
