Anti-Cheat #1: If you are using university computers to do the exams, you can always use a key-logger/screen-logger - so you know exactly what information they search for. Though open information and privacy are huge concerns in every day life, try to find a way to explain the need of Internet privacy during an open Internet exam. You must of course, pre-warn them that if they access their own email or any site with passwords, that snapshots will be recorded, as will be their passwords, etc.
Anti-Cheat Backup: This should go with #1, but used separately if #1 proves too difficult or if there is somehow a privacy issue even during an exam (oh, i just thought of one - my fingers slipped 104 times in a row and sent an email to a friend with the exact question i needed answering and got a response quickly was pure coincidence and I couldn't possibly not write down that answer since that was what I was going to write anyway!). Anyway, the back-up: don't install one, but SAY it's installed (be sure to go on about the name of the software, developed by X-high-tech-company-just-for-universities, what kind of new technology that has gone into them, how it's code is updated quarterly, and be sure to emphasize that every single keystroke makes a difference and can be used as official evidence for expulsion in the case of cheating).
Ways to Cheat: Photo cryptography may go undetected in some situations, though it's difficult when you have a key-logger present in the case of two-way transmission. One way cryptography is possible, though also difficult (If the list of answers to all questions exist in photos somewhere good for them.) (two-way is not practical -> the student can't send without typing keys - unless he uses a Ceasar cipher or something that is relatively quickly broken. Any other cipher for that matter, though this is already a huge red-flag in the first place if they aren't typing an accepted language or are using obvious code wording (What does the Gangster mean daddy when he says "The duck is about to lose its feathers..."?) Another crack, if someone uses something like a wiretap (leaving a phone on or other device) so the listener can hear the question and post a page. student could write every question on the screen as well while another 'listener' is watching (which is relatively easy if there's a pre-agreed upon site or by listening in on the phone), post the site relatively hidden on another pre-agreed upon website after x-minutes - and do this in of a pre-agreed upon cipher (such as the first word of each sentence is the solution (or more obscure than this if they are hard-working enough)). I think that's a good start - and unless I'm missing something obvious, it is about as tough to cheat, if not tougher, than current exams (university computers are relatively secure, and no phones allowed during exams - oh i guess hidden phone may be another one, but that's general cheating related, not open Internet test). Someone may find another way, at which time that knowledge can be used to thwart future use of that method, or discontinue it's use if it's a devastating one.