  The first gravitational-wave (GW) observations will greatly benefit from the
detection of coincident electromagnetic counterparts. Electromagnetic
follow-ups will nevertheless be challenging for GWs with poorly reconstructed
directions. GW source localization can be inefficient (i) if only two GW
observatories are in operation; (ii) if the detectors' sensitivities are highly
non-uniform; (iii) for events near the detectors' horizon distance. For these
events, follow-up observations will need to cover 100-1000 square degrees of
the sky over a limited period of time, reducing the list of suitable
telescopes. We demonstrate that the Cherenkov Telescope Array will be capable
of following up GW event candidates over the required large sky area with
sufficient sensitivity to detect short gamma-ray bursts, which are thought to
originate from compact binary mergers, out to the horizon distance of advanced
LIGO/Virgo. CTA can therefore be invaluable starting with the first
multimessenger detections, even with poorly reconstructed GW source directions.
This scenario also provides a further scientific incentive for GW observatories
to further decrease the delay of their event reconstruction.
