Atomic-Clock.org.uk has a wide selection of watches and clocks that are radio controlled and always set to the exact second. Radio controlled watches and clocks (both mostly quartz driven) receive a radio signal (in Europe mostly DCF77 out of Frankfurt, Germany, in Britain its is the MSF60 out of Anthorn in Cumbria) by which they automatically set themselves regularly down to a millisecond.
The radio controlled watch was invented and patented by Wolfgang Hilberg for the German company Telefunken in 1967. Multi frequency watches (such as Junghans, Casio, Seiko and Citizen) can synchronize with most time signals in Europe, Britain, Japan and the US. Other radio controlled watches can be offset from their time signal, so a radio controlled watch from Europe can be set at -1 hrs to display GMT (the transmitters in Europe and Britain are effective to over 1500 kilometres, so reception is not an issue).
When buying a radio controlled watch, please watch which time signals it can receive and if these signals are available in your area.