Tides are a key component in coastal extreme water levels. Possible changes in the tides caused by mean sea-level rise (SLR) are therefore of importance in the analysis of coastal flooding, as well as many other applications. We investigate the effect of future SLR on the tides globally using a fully global forward tidal model: OTISmpi. Statistical comparisons of the modelled and observed tidal solutions demonstrate the skill of the refined model setup with no reliance on data assimilation. We simulate the response of the four primary tidal constituents to various SLR scenarios. Particular attention is paid to future changes at the largest 136 coastal cities, where changes in water level would have the greatest impact. Spatially uniform SLR scenarios ranging from 0.5 to 10 m with fixed coastlines show that the tidal amplitudes in shelf seas globally respond strongly to SLR with spatially coherent areas of increase and decrease. Changes in the M2 and S2 constituents occur globally in most shelf seas, whereas changes in K1 and O1 are confined to Asian shelves. With higher SLR tidal changes are often not proportional to the SLR imposed and larger portions of mean high water (MHW) changes are above proportional. Changes in MHW exceed ±10% of the SLR at ~10% of coastal cities. SLR scenarios allowing for coastal recession tend increasingly to result in a reduction in tidal range. The fact that the fixed and recession shoreline scenarios result mainly in changes of opposing sign is explained by the effect of the perturbations on the natural period of oscillation of the basin. Our results suggest that coastal management strategies could influence the sign of the tidal amplitude change. The effect of a spatially varying SLR, in this case fingerprints of the initial elastic response to ice mass loss, modestly alters the tidal response with the largest differences at high latitudes.