PSR J0218+4232 is one of the most energetic millisecond pulsars known and has long been considered as one of the best candidates for very high-energy (VHE; >100 GeV) gamma-ray emission. Using 11.5 years of Fermi Large Area Telescope (LAT) data between 100 MeV and 870 GeV, and ~90 hours of MAGIC observations in the 20 GeV to 20 TeV range, we have searched for the highest energy gamma-ray emission from PSR J0218+4232. Based on the analysis of the LAT data, we find evidence for pulsed emission above 25 GeV, but see no evidence for emission above 100 GeV (VHE) with MAGIC. We present the results of searches for gamma-ray emission, along with theoretical modeling, to interpret the lack of VHE emission. We conclude that, based on the experimental observations and theoretical modeling, it will remain extremely challenging to detect VHE emission from PSR J0218+4232 with the current generation of Imaging Atmospheric Cherenkov Telescopes (IACTs), and maybe even with future ones, such as the Cherenkov Telescope Array (CTA).