This paper explores the behaviour of the ubiquitous twisted pairs at high frequencies and wideband excitation of twisted pairs up to 12GHz. Although there is a large quantity of papers on twisted pairs, the papers in the literature mostly focus on the sub-1GHz spectrum, where the current digital subscriber line technologies operate. Higher carrier frequencies on twisted pairs can enable the data rates required by the future communication networks; hence, the existing copper infrastructure can be utilised on the last mile complementing the fibre networks. Towards this objective, we derive analytical expression for the electromagnetic fields and characteristic equation of twisted pairs. With these derivations we show a fundamental limit on the operating frequency of twisted pairs beyond which twisted pairs start to radiate and behave like an antenna. To validate our theory through measurements, we designed a microstrip balun in order to excite the differential mode on the twisted pairs. Unlike off-the-shelf devices, this balun has a nearly linear transmission curve across 1-12GHz. This linearity allows us to detect the radiation which would not have been possible with an off-the-shelf device. At the end, we demonstrate that the standard twisted pairs used in the UK can be used up to 5GHz carrier frequency without any radiation effect and this upper-bound can be moved to higher frequencies by decreasing the twist lengths.