Modern maritime microgrid systems are witnessing a revolutionary advancement by integrating more renewable energy sources and energy storage systems. The integration of these sophisticated systems is achieved, however, through the power electronics converters that cause severe harmonic contamination. This problem becomes more serious when some of these harmonics that are non-integer multiples of the fundamental (inter-harmonics) exist concurrently with both system frequency drifts and large-power transients, which is a commune issue in maritime microgrid systems such as shipboard microgrids. Hence, the performance of the widely signal processing algorithms applied in the measurement and communication systems such as the smart meters and power quality analyzers tends to worsen. To address this problem this paper proposes an effective method based on the eigenvalue solution to estimate the harmonics and inter-harmonics of modern maritime microgrid systems effectively. This method, which is a system frequency independent technique can work effectively even under large frequency drifts with short window width. The proposed method is evaluated under MATLAB software, and then the experimental validation is carried out via analyzing the electrical power system current of a bulk carrier ship.