The bimodality in observed present-day galaxy colours has long been a challenge for hierarchical galaxy formation models, as it requires some physical process to quench (and keep quenched) star formation in massive galaxies. Here we examine phenomenological models of quenching by post-processing the star formation histories of galaxies from cosmological hydrodynamic simulations that reproduce observations of star-forming galaxies reasonably well. We consider recipes for quenching based on major mergers, halo mass thresholds, gas temperature thresholds, and variants thereof. We compare the resulting simulated star formation histories to observed g-r colour-magnitude diagrams and red and blue luminosity functions from SDSS. The merger and halo mass quenching scenarios each yield a distinct red sequence and blue cloud of galaxies that are in broad agreement with data, albeit only under rather extreme assumptions. In detail, however, the simulated red sequence slope and amplitude in each scenario is somewhat discrepant, perhaps traceable to low metallicities in simulated galaxies. Merger quenching produces more massive blue galaxies, earlier quenching, and more frosting of young stars; comparing to relevant data tends to favor merger over halo mass quenching. Although physically-motivated quenching models can produce a red sequence, interesting generic discrepancies remain that indicate that additional physics is required to reproduce the star formation and enrichment histories of red and dead galaxies.