Perform the test in telepathy-proof rooms
To prevent ESP related problems the test would have to be carried out in "telepathy-proof" rooms.
The Turing Argument"If telepathy is admitted it will be necessary to tighten our test up. The situation could be regarded as analogous to that which would occur if the interrogator were talking to himself and one of the competitors was listening with his ear to the wall. To put the competitors into a 'telepathy-proof room' would satisfy all requirements" (Turing, 1950).
Source: Turing, A.M. (1950) "Computing Machinery and Intelligence" Mind, 59, 433-60.