The detection of the New Moon at sunset is of importance to communities based on the lunar calendar. This is traditionally undertaken with visual observations. We propose a radio method which allows a higher visibility of the Moon relative to the Sun and consequently gives us the ability to detect the Moon much closer to the Sun than is the case of visual observation. We first compare the relative brightness of the Moon and Sun over a range of possible frequencies and find the range 5--100\,GHz to be suitable. The next consideration is the atmospheric absorption/emission due to water vapour and oxygen as a function of frequency. This is particularly important since the relevant observations are near the horizon. We show that a frequency of $\sim 10$ GHz is optimal for this programme. We have designed and constructed a telescope with a FWHM resolution of 0$^\circ{}\!\!$.6 and low sidelobes to demonstrate the potential of this approach. At the time of the 21 May 2012 New Moon the Sun/Moon brightness temperature ratio was $72.7 \pm 2.2$ in agreement with predictions from the literature when combined with the observed sunspot numbers for the day. The Moon would have been readily detectable at $\sim 2^{\circ}$ from the Sun. Our observations at 16\,hr\,36\,min UT indicated that the Moon would have been at closest approach to the Sun 16\,hr\,25\,min earlier; this was the annular solar eclipse of 00\,hr\,00\,min\,UT on 21 May 2012.

11 pages, 15 figures, accepted for publication in MNRAS