Concorde used to display a CG position throughout flight.
This calculation was done by a CG computer (of which there were actually three) which monitored fuel tank quantities and distribution, and, based on initial zero fuel weight and CG entries, displayed the CG position.
Although this was accepted as being reasonably accurate, Mad (Flt) Scientist is quite correct to say that this was really just an estimate of the CG position, rather than a measurement or calculation of it.
One of the more demanding abnormal procedures for the F/E was to alter/monitor the aircraft CG position, by means of fuel transfer, following a triple CG computer failure, particularly during the deceleration and descent from supercruise to subsonic flight.
This usually involved many muttered comments about the parentage of the avionic engineers responsible for maintaining said computers, coupled with not quite so muttered comments about the inabilty of his pilots to fly at exactly the speeds he wanted, when he wanted!
However, despite these shortcomings, and despite having to use various charts and graphs, when later viewed on the FDR or simulator trace, the movement of the CG always seemed to have gone better than when the CG computers were available!
In reality, as Loose rivets suggests, provided the aircraft Mach number was known accurately, the position of the elevons, as displayed on the control position indicator, was considered at least as good an indicator of CG position as the CG computer derived position!