  We present a framework to obtain photometric redshifts (photo-zs) for
gamma-ray burst afterglows. Using multi-band photometry from GROND and
Swift/UVOT, photo-zs are derived for five GRBs for which spectroscopic
redshifts are not available. We use UV/optical/NIR data and synthetic
photometry based on afterglow observations and theory to derive the photometric
redshifts of GRBs and their accuracy. Taking into account the afterglow
synchrotron emission properties, we investigate the application of photometry
to derive redshifts in a theoretical range between z~1 and z~12. The
measurement of photo-zs for GRB afterglows provides a quick, robust and
reliable determination of the distance scale to the burst, particularly in
those cases where spectroscopic observations in the optical/NIR range cannot be
obtained. Given a sufficiently bright and mildly reddened afterglow, the
relative photo-z accuracy is better than 10% between z=1.5 and z~7 and better
than 5% between z=2 and z=6. We detail the approach on 5 sources without
spectroscopic redshifts observed with UVOT on-board Swift and/or GROND. The
distance scale to those same afterglows is measured to be
$z=4.31^{+0.14}_{-0.15}$ for GRB 080825B, $z=2.13^{+0.14}_{-0.20}$ for GRB
080906, $z=3.44^{+0.15}_{-0.32}$ for GRB 081228, $z=2.03^{+0.16}_{-0.14}$ for
GRB 081230 and $z=1.28^{+0.16}_{-0.15}$ for GRB 090530. Combining the response
from UVOT with ground-based observatories and in particular GROND operating in
the optical/NIR wavelength regime, reliable photo-zs can be obtained from z ~
1.0 out to z ~ 10, and possibly even at higher redshifts in some favorable
cases, provided that these GRBs exist, are localized quickly, have sufficiently
bright afterglows and are not heavily obscured.
