After many years of successful operation, the JET saddle coil system was dismantled during the 2004-2005 shutdown. Due to their geometry, the saddle coils could drive only low toroidal mode numbers, |n| = 0-2. Conversely, the Alfvén Eigenmodes (AEs) that can be driven unstable in JET (and ITER) by fusion generated alphas or other fast particles have toroidal mode numbers in the range n~5-20. This, and because most of the previous JET measurements were obtained in plasmas with low edge magnetic shear, makes it difficult to extrapolate the low-n results to ITER. These reasons prompted the design of a new system of compact antennas for excitation and measurements of high-n modes. In this paper we review the antenna design principles and present the first measurements of the frequency and damping rate for n~1-10 AEs obtained with this new antenna system. These data have been obtained not only in limited plasmas, but also in ITER-relevant X-point plasma configurations with high edge magnetic shear and moderate heating power.