You are correct. Short read sequencing as well as microarrays are essentially blind to whole genome duplication events.
Interestingly, the best technologies for this goal are much older, when the study of genetics needed to leverage both visual signals and molecular techniques.
1) Karyotyping
2) FISH
Why does that help? Well, because both these technologies confer ability to view genomic elements within the context of the cells that house them. As such, the ploidy of the cell can be determined for instance by counting the number of condensed chromosomes inside a single cell. For the same reason, these technologies also enable correlation of morphological characteristics of cells to such genomic variants. The trade-off is that, as a result, the structural variant has to be large enough to be viewed under a microscope - at minimum dozens of kb to Mb or larger.
Additionally, it is likely that third generation sequencing tech (i.e. single molecule, real-time, long-read techniques) such as ZMW and nanopore-based sequencing (PacBio, Oxford Nanopore) will be able to detect WGDs, though I am not sure this has been shown yet. Here, I'm referring to the ability of both to detect epigenetic modifications to DNA in addition to primary sequence.