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Strong gravitational lensing of supernovae is exceedingly rare. To date, onlya handful of lensed supernovae are known. Despite this, lensed supernovae haveemerged as a promising method for measuring the current expansion rate of theUniverse and breaking the Hubble tension. We present an extensive search forgravitationally lensed supernovae within the Zwicky Transient Facility (ZTF)public survey, covering 15,215 transients with good light curves discoveredduring four years of observations. We crossmatch a catalogue of known andcandidate lens galaxies with our sample and find three coincident sources,which were due to chance alignment. To search for supernovae magnified byunknown lenses, we test multiple methods suggested in the literature for thefirst time on real data. This includes selecting objects with extremely redcolours, those that appear inconsistent with the host galaxy redshift, andthose with bright absolute magnitudes inferred from the host galaxy redshift.We find a few hundred candidates, most of which are due to contamination fromactivate galactic nuclei, bogus detections, or unlensed supernovae. The falsepositive rate from these methods presents significant challenges for futuresurveys. In total, 132 unique transients were identified across all of ourselection methods that required detailed manual rejection, which would beinfeasible for larger samples. Overall, we do not find any compellingcandidates for lensed supernovae, which is broadly consistent with previousestimates for the rate of lensed supernovae from the ZTF public survey aloneand the number expected to pass the selection cuts we apply.

A search for gravitationally lensed supernovae within the Zwicky Transient Facility public survey