This paper considers the single machine scheduling problem with weighted quadratic tardiness costs. Three metaheuristics are presented, namely iterated local search, variable greedy and steady-state genetic algorithm procedures. These address a gap in the existing literature, which includes branch-andbound algorithms (which can provide optimal solutions for small problems only) and dispatching rules (which are efficient and capable of providing adequate solutions for even quite large instances). A simple local search procedure which incorporates problem specific information is also proposed. The computational results show that the proposed metaheuristics clearly outperform the best of the existing procedures. Also, they provide an optimal solution for all (or nearly all, in the case of the variable greedy heuristic) the smaller size problems. The metaheuristics are quite close in what regards solution quality. Nevertheless, the iterated local search method provides the best solution, though at the expense of additional computational time. The exact opposite is true for the variable greedy procedure, while the genetic algorithm is a good all-around performer.