A method and device for recovering drilling fluid used in connection with the provision of a subsea well, in which the drilling fluid is circulated from a vessel on a sea surface via a drill string and out through a drill bit into an annulus which is defined by a borehole and the drill string. The device includes a filtering device which is connected, in respect of fluid, to an annulus and which is arranged to contain drill cuttings and drilling fluid. A fluid line extends from a portion of the filtering device to the vessel, the fluid line being arranged to carry drilling fluid which has been separated from the drill cuttings back to the vessel.