The invention provides a supply unit (10, 20) for liquid medical oxygen, the supply unit (10, 20) including a reservoir (11, 21) adapted to be filled with the liquid medical oxygen, at least one dispensing valve (13, 19, 23) in fluid communication with the reservoir (11, 21) and operable by a user of the supply unit (10, 20), and an overpressure valve (14, 24) in fluid communication with the reservoir (11, 21) and adapted to open in order to vent the reservoir (11, 21) when a pressure in the reservoir (11, 21) exceeds a given value. The mobile supply unit (10, 20) includes estimating means adapted to provide a value corresponding to an amount of the liquid medical oxygen spent from the reservoir (11, 21) since an initial timepoint at least on the basis of a value corresponding to an initial amount of the liquid medical oxygen in the reservoir (11, 21) at the initial timepoint, a value corresponding to one or more valve settings of the dispensing valve or valves (13, 19, 23) since the initial timepoint, and a value corresponding to one or more durations during which the overpressure valve (14, 24) was open in order to vent the reservoir (11, 21) since the initial timepoint. A corresponding method is also part of the present invention.