The opacity property characterizes the absence of confidential information flow towards inquisitive attackers. Verifying opacity is well established for finite automata but is known to be not decidable for more expressive models like Turing machines or Petri nets. As a consequence, for a system dealing with confidential information, certifying its confidentiality may be impossible, but attackers can infer confidential information by approximating systems' behaviours. Taking such attackers into account, we investigate the verification of opacity using abstraction techniques to compute executable counterexamples (attack scenarios). Considering a system and a predicate over its executions, attackers are modeled as semi-conservative decision process determining from observed traces the truth of that predicate. Moreover, we will show that the most precise the abstraction is, the most accurate (and then dangerous) the corresponding class of attackers will be. Consequently, when no attack scenario is detected on an approximate analysis, we know that this system is safe against all ``less precise'' attackers. This can therefore be used to provide a level of certification relative to the precision of abstractions.