  We evaluate the broadband afterglow emission of very high redshift gamma-ray
bursts (GRBs) using standard relativistic blastwave models with both forward
and reverse shock components. For a broad range of parameters, a generic
property for GRBs at redshifts $z \sim$ 5--30 is that the emission peaks in the
millimeter to far-infrared bands with milli-Jansky flux levels, first at a few
hours after the burst due to the reverse shock, and then again for several days
afterwards with somewhat lower flux due to the forward shock. The radio,
submillimeter and infrared continuum emission should be readily detectable out
to $z \ga 30$ by the Atacama Large Millimeter Array (ALMA), Extended Very Large
Array (EVLA), Square Kilometer Array (SKA) and other facilities. For relatively
bright bursts, spectroscopic measurements of molecular and atomic absorption
lines due to ambient protostellar gas may be possible. Utilizing models of
primordial protostellar clouds, we show that under certain conditions,
appreciable absorption may be caused by HD rotational transitions even in
metal-free environments. After sufficient metal enrichment, absorption from CO
rotational transitions and [OI] fine-structure transitions can also become
strong. With appropriate observing strategies in combination with optical
telescopes, ALMA and/or SKA may be able to detect such lines, offering a unique
probe of physical conditions in individual Pop III and early Pop II star
forming regions. We also remark on potential near-infrared absorption features
due to electronic transitions of H$_2$.
