The sources of ultra-high energy cosmic rays (UHECRs) are still one of the main open questions in high-energy astrophysics. If UHECRs are accelerated in astrophysical sources, they are expected to produce high-energy photons and neutrinos due to the interaction with the surrounding astrophysical medium or ambient radiation. In particular, neutrinos are powerful probes for the investigation of the region of production and acceleration of UHECRs since they are not sensitive to magnetic deflections nor to interactions with the interstellar medium. The results of three different analyses that correlate the very high-energy neutrino candidates detected by IceCube and ANTARES and the highest-energy cosmic rays measured by the Pierre Auger Observatory and the Telescope Array will be discussed. The first two analyses use a sample of high-energy neutrinos from IceCube and ANTARES selected to have a significant probability to be of astrophysical origin. The first analysis cross-correlates the arrival directions of these selected neutrino events and UHECRs. The second one is a stacked likelihood analysis assuming as stacked sources the high-energy neutrino directions and looking for excesses in the UHECR data set around the directions of the neutrino candidates. The third analysis instead uses a larger sample of neutrinos selected to look for neutrino point-like sources. It consists of a likelihood method that looks for excesses in the neutrino point-source data set around the directions of the highest-energy UHECRs.