Cecil’s updated post on this topic, http://www.straightdope.com/columns/read/2390/do-crocodiles-shed-tears-revisited, states that there is no physiological basis for crocodile tears. Obviously the old tale that crocodiles pretend to weep for the creatures they eat is false; the question is whether there is something that appears to be tears.
Contrary to Simon on Crocodiles & Alligators, quoted in the question to Cecil, the Crocodilian Biology Database, http://crocodilian.com/cnhc/cbd-faq-q6.htm, states that crocodiles do have lachrymal glands that produce tears, much like human lachrymal glands. (Actually, Simon says that crocodiles do not have tear ducts, not that they do not have lachrymal glands; I don’t know if that’s an important distinction.) According to a 2007 report from the University of Florida, http://news.ufl.edu/archive/2007/10/researchers-no-faking-it-crocodile-tears-are-real.html, crocodilians do tend to tear up when eating; the researchers speculate that this is because the animals hiss and huff while they eat. The researchers used caimans and alligators rather than crocodiles, for reasons of convenience.