of observing a higher-redshift, gravitationally magnified (amplified) supernova.

Searching for lensed supernovae via image multiplicity or magnification are the main observational strategies based on two characteristic features of the lensing phenomenon. The expected discovery rates have been estimated in several studies; however, each of them considering only one of the two methods and adopting specifications of upcoming surveys [@Ogu2010a; @Gold2017; @Gold2018]. At present, it is unclear to what extent the two methods are equivalent or complementary, which technique is more effective in finding lensed supernovae in different ranges of limiting magnitudes or whether one would benefit from combining them. The two methods may differ not only in terms of their performance in finding candidates, but also in terms of the characteristics of the resulting lensed supernova samples. This in turn raises the question which supernova sample and thus which method would be suitable for robust measurements of time delays for the purpose of cosmological inference. In order to address these issues, we compute detection rates for both methods and a wide range of possible filters and supernova types. This allows us to make the first comprehensive comparison of detection methods in terms of the discovery potential and the cosmological constraining 