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Electrically conductive seawater, moving in an ambient magnetic field, generates electromagnetic (EM) variations. Tsunamis are significant contributors to this phenomenon, inducing observable electric and magnetic fluctuations at seafloor and coastal observatories. While understanding of these occurrences in open oceans is robust, knowledge regarding their observation on islands remains limited. This article seeks, through the use of numerical experimentation, to enhance our understanding of tsunami-generated EM (TGEM) variations observed on islands. Utilizing simulations involving conical islands, we identify three key insights regarding EM intensity normalized by the height of incident tsunamis: (i) increased ocean depth surrounding the island amplifies tsunami EM signals, particularly for periods shorter than 20 min; (ii) magnetic field strength at the island is approximately comparable to that observed at the seafloor in the absence of the island when the island radius is smaller than 6 km; and (iii) electric field intensity at the island notably surpasses that observed at the seafloor, especially with smaller island radii (≤ 6 km). Additionally, we establish that employing the ratio of island radius to tsunami wavelength near the island coast facilitates the derivation of empirical functions for this phenomenon. This article is part of the theme issue 'Magnetometric remote sensing of Earth and planetary oceans'. [ABSTRACT FROM AUTHOR]