Motivated by discovering strongly lensed supernovae, gravitational waves, and kilonovae in the 2020s, we investigate whether to build a watchlist of clusters based on observed cluster properties (i.e. lens-plane selection) or on the detectability of strongly lensed background galaxies (i.e. source-plane selection). First, we estimate the fraction of high-redshift transient progenitors that reside in galaxies that are themselves too faint to be detected as being strongly lensed. We find ∼15–50 per cent of transient progenitors reside in z = 1 − 2 galaxies too faint to be detected in surveys that reach AB ≃ 23, such as the Dark Energy Survey. This falls to ≲10 per cent at depths that will be probed by early data releases of LSST (AB ≃ 25). Secondly, we estimate a conservative lower limit on the fraction of strong-lensing clusters that will be missed by magnitude-limited searches for multiply imaged galaxies and giant arcs due to the faintness of such images. We find that DES-like surveys will miss ∼75 per cent of 1015 M⊙ strong-lensing clusters, rising to ∼100 per cent of 1014 M⊙ clusters. Deeper surveys, such as LSST, will miss ∼40 per cent at 1015 M⊙ and ∼95 per cent at 1014 M⊙. Our results motivate building a cluster watchlist for strongly lensed transients that includes those found by the lens-plane selection.