Magnetic (or tidal) interactions between "hot Jupiters" and their host stars can potentially enhance chromospheric and coronal activity. An ideal test bed for investigating this effect is provided by the extreme WASP-18 system, which features a massive (~10 times Jupiter) close-in (lsim1 day period) transiting planet orbiting a young F6 star. Optical and X-ray observations of WASP-18 were conducted in 2011 November. The high-resolution echelle spectrograph Magellan Inamori Kyocera Echelle was used on the 6.5 m Magellan Clay Telescope to obtain 13 spectra spanning planetary orbital phases of 0.7-1.4, while the X-ray Telescope on Swift provided contemporaneous monitoring with a stacked exposure of ~50 ks. The cores of the Ca II H and K lines do not show significant variability over multiple orbits spanning ~8 days, in contrast to the expectation of phase-dependent chromospheric activity enhancements for efficient star-planet interaction. The star is also X-ray faint, with log L X < 27.6, indicating that coronal activity is likewise low. The lack of detectable star-planet interaction in this extreme system requires that any such effect here must be transient, if indeed present. We demonstrate that searches for Ca II H and K variability can potentially mistake a stellar hotspot, if observed over a short segment of the rotation period, for planet-induced activity. Taken together, these results suggest that the utility of star-planet interaction as a robust method of estimating exoplanet magnetic field strengths may be limited.