Latvala and Heljanko have presented how model checking of linear temporal logic properties of P/T nets with fairness constraints on the transitions can be done efficiently. In this work the procedure is extended to high-level Petri Nets, Coloured Petri Nets in particular. The model checking procedure has been implemented in the Maria tool. As a case study, a liveness property of a sliding window protocol is model checked. The results indicate that the procedure can cope well with many fairness constraints, which could not have been handled by specifying the constraints as a part of the property to be verified.