Optimization in sports is a field of increasing interest. Combinatorial optimization techniques have been applied e.g. to game scheduling and playoff elimination. A problem that arises in competition management is the assignment of referees to games already scheduled. There are a number of rules and objectives that should be taken into account when referees are assigned to games. We address two mono-objective versions of a Referee Assignment Problem (RAP) common to many amateur leagues of sports such as soccer, baseball, and basketball. The problem is formulated by integer programming and its decision version is proved to be NP-complete. To tackle real-life large instances of the RAP, we propose a three-phase heuristic approach based on a constructive procedure, a repair heuristic to make solutions feasible, and a local search heuristic to improve feasible solutions, based on the metaheuristic iterated local search. Numerical results on realistic instances are presented and discussed. This work also investigates the solution of a bi-objective version of the RAP, which combines both objective functions used in the mono-objective versions. Exact and heuristic approaches are proposed to solve this bi-objective version and its computational results are discussed.