ABSTRACT Recent observations indicate that in a large fraction of binary neutron star (BNS) mergers a long-lived neutron star (NS) may be formed rather than a black hole. Unambiguous electromagnetic (EM) signatures of such a scenario would strongly impact our knowledge on how short gamma-ray bursts (SGRBs) and their afterglow radiation are generated. Furthermore, such EM signals would have profound implications for multimessenger astronomy with joint EM and gravitational-wave (GW) observations of BNS mergers, which will soon become reality thanks to the ground-based advanced LIGO/Virgo GW detector network. Here we explore such EM signatures based on the model presented in a companion paper, which provides a self-consistent evolution of the post-merger system and its EM emission up to ∼107 s. Light curves and spectra are computed for a wide range of post-merger physical properties. We present X-ray afterglow light curves corresponding to the "standard" and the "time-reversal" scenario for SGRBs (prompt emission associated with the merger or with the collapse of the long-lived NS). The light curve morphologies include single and two-plateau features with timescales and luminosities that are in good agreement with Swift observations. Furthermore, we compute the X-ray signal that should precede the SGRB in the time-reversal scenario, the detection of which would represent smoking-gun evidence for this scenario. Finally, we find a bright, highly isotropic EM transient peaking in the X-ray band at ∼102-104 s after the BNS merger with luminosities of LX ∼ 1046-1048 erg s−1. This signal represents a very promising EM counterpart to the GW emission from BNS mergers.