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This paper investigates the effectiveness of various methods to accelerate the convergence to a steady state in time-periodic electromagnetic field problems. We first introduce the time-periodic explicit error correction (TP-EEC) method taking account of both the dc and linearly-varying error components and propose the harmonics TP-EEC method which enables us to achieve the increase in error correction frequency. Then, we discuss the convergence property of the TP-EEC methods based on the error analysis. The advantages and disadvantages of the TP-EEC method and the time differential correction (TDC) method are investigated from the viewpoints of computational costs and application scope.