  We report the results of high-field, low-temperature MuSR measurements of the
quasi two-dimensional organic superconductors \k{appa}-(ET)2Cu(NCS)2 and
\k{appa}-(ET)2Cu[N(CN)2]Br. The MuSR lineshapes for these compounds indicate
the existence of partially-ordered vortex lattice phases in the high magnetic
field regime, up to 2.5 T for the former compound and 4 T for the latter
compound. The observed sharp loss of order is found to be consistent with a
vortex-lattice melting transition that is predicted by numerical simulations of
weakly coupled layers of pancake vortices. It is argued that the robustness of
the partially-ordered vortex lattice phases could be due to strong flux-line
pinning by a dilute ensemble of defects.
