We forecast the abilities of the Atacama Large Millimeter/submillimeter Array (ALMA) and the Square Kilometer Array (SKA) to detect CO and Hi emission lines in galaxies at redshift z = 3. A particular focus is set on Milky Way (MW) progenitors at z = 3 since their detection within 24 hr constitutes a key science goal of ALMA. The analysis relies on a semi-analytic model, which permits the construction of an MW progenitor sample by backtracking the cosmic history of all simulated present-day galaxies similar to the real MW. Results are as follows: (1) ALMA can best observe an MW at z = 3 by looking at CO(3-2) emission. The probability of detecting a random model MW at 3 sigma in 24 hr using 75 km s(-1) channels is roughly 50%, and these odds can be increased by co-adding the CO(3-2) and CO(4-3) lines. These lines fall into ALMA band 3, which therefore represents the optimal choice toward MW detections at z = 3. (2) Higher CO transitions contained in the ALMA bands >= 6 will be invisible, unless the considered MW progenitor coincidentally hosts a major starburst or an active black hole. (3) The high-frequency array of SKA, fitted with 28.8 GHz receivers, would be a powerful instrument for observing CO(1-0) at z = 3, able to detect nearly all simulated MWs in 24 hr. (4) Hi detections in MWs at z = 3 using the low-frequency array of SKA will be impossible in any reasonable observing time. (5) SKA will nonetheless be a supreme Hi survey instrument through its enormous instantaneous field of view (FoV). A one-year pointed Hi survey with an assumed FoV of 410 deg(2) would reveal at least 10(5) galaxies at z = 2.95-3.05. (6) If the positions and redshifts of those galaxies are known from an optical/infrared spectroscopic survey, stacking allows the detection of Hi at z = 3 in less than 24 hr.