The ANtarctic Impulse Transient Antenna (ANITA) is the first long-duration balloon experiment designed to search and measure the flux of Greisen- Zapsepin-Kuzmin (GZK) neutrinos. We present new limits on neutrinos fluxes of astronomical origin from data collected with the successful launch of a 2- antenna prototype instrument, called ANITA-lite, that circled the Antarctic continent for 18.4 days in January 2004. We performed a search for Ultra- High-Energy (UHE) neutrinos with energies above 3 x 1018 eV. No excess events above the background expectation were observed and a neutrino flux following E-2 spectrum for all neutrino flavors, is limited to Ev-2F < 1.6 × 10-6 GeV cm-2 s-1 sr-1 for 1018.5 eV < Ev < 1023.5 eV at 90% confidence level. The launch of ANITA is scheduled for December 2006. Looking beyond ANITA, we describe a new idea, called ARIANNA (Antarctic Ross Iceshelf ANtenna Neutrino Array), to increase the sensitivity for GZK neutrinos by one order of magnitude better than ANITA.