  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 for their detection within 24 h constitutes a key science
goal of ALMA. The analysis relies on a semi-analytic model, which permits the
construction of a MW progenitor sample by backtracking the cosmic history of
all simulated present-day galaxies similar to the real MW. Results: (i) ALMA
can best observe a MW at z=3 by looking at CO(3-2) emission. The probability of
detecting a random model MW at 3-sigma in 24 h using 75 km/s 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 towards MW detections at z=3. (ii) Higher CO transitions
contained in the ALMA bands geq6 will be invisible, unless the considered MW
progenitor coincidentally hosts a major starburst or an active black hole.
(iii) 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 h. (iv) HI detections in MWs at z=3 using the low-frequency
array of SKA will be impossible in any reasonable observing time. (v) SKA will
nonetheless be a supreme ha survey instrument through its enormous
instantaneous field-of-view (FoV). A one year pointed HI survey with an assumed
FoV of 410 sqdeg would reveal at least 10^5 galaxies at z=2.95-3.05. (vi) 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 h.
