There is evidence that the ozone layer has begun to recover owing to the ban on the production of halogenated ozone-depleting substances (hODS) accomplished by the Montreal Protocol and its amendments and adjustments (MPA). However, recent studies, while reporting an increase in tropospheric ozone from the anthropogenic NOx and CH4 and confirming the ozone recovery in the upper stratosphere from the effects of hODS, also indicate a continuing decline in the lower tropical and mid-latitudinal stratospheric ozone. While these are indications derived from observations, they are not reproduced by current global chemistry–climate models (CCMs), which show positive or near-zero trends for ozone in the lower stratosphere. This makes it difficult to robustly establish ozone evolution and has sparked debate about the ability of contemporary CCMs to simulate future ozone trends. We applied the new Earth system model (ESM) SOCOLv4 (SOlar Climate Ozone Links, version 4) to calculate long-term ozone trends between 1985–2018 and compare them with trends derived from the BAyeSian Integrated and Consolidated (BASIC) ozone composite and MERRA-2, ERA-5, and MSRv2 reanalyses. We designed the model experiment with a six-member ensemble to account for the uncertainty of the natural variability. The trend analysis is performed separately for the ozone depletion (1985–1997) and ozone recovery (1998–2018) phases of the ozone evolution. Within the 1998–2018 period, SOCOLv4 shows statistically significant positive ozone trends in the mesosphere, upper and middle stratosphere, and a steady increase in the tropospheric ozone. The SOCOLv4 results also suggest slightly negative trends in the extra-polar lower stratosphere, yet they barely agree with the BASIC ozone composite in terms of magnitude and statistical significance. However, in some realizations of the SOCOLv4 experiment, the pattern of ozone trends in the lower stratosphere resembles much of what is observed, suggesting that SOCOLv4 may be able to reproduce the observed trends in this region. Thus, the model results reveal marginally significant negative ozone changes in parts of the low-latitude lower stratosphere, which agrees in general with the negative tendencies extracted from the satellite data composite. Despite the slightly smaller significance and magnitude of the simulated ensemble mean, we confirm that modern CCMs such as SOCOLv4 are generally capable of simulating the observed ozone changes, justifying their use to project the future evolution of the ozone layer.