This is a surprisingly tricky question. It turns out sea level is much less of a static benchmark than we might imagine. Past efforts to measure long-term trends in sea level have been frustrating. For example, even if sea level is not changing, land level often is, via subsidence or the reverse. The IPCC famously drew some of its most catastrophic sea level predictions from tide gages in Hong Kong that are on land that is sinking (thus imparting an artificial sea level rise in the data).
The article is published in Geophysical Research Letters, the authors are from Tulane University and the State University of New York at Stony Brook, and the work was not funded by any horrible industry group. Kolker and Hameed begin their article stating “Determining the rate of global sea level rise (GSLR) during the past century is critical to understanding recent changes to the global climate system. However, this is complicated by non-tidal, short-term, local sea-level variability that is orders of magnitude greater than the trend.”
Once again, we face the dual problems in climate measurement of 1. Sorting through long-term cyclical changes and 2. Very low signal to noise ratio in climate change data.
The authors further note that “Estimates of recent rates of global sea level rise (GSLR) vary considerably” noting that many scientists have calculated rates of 1.5 to 2.0 mm per year over the 20th century. They also show that other very credible approaches have led to a 1.1 mm per year result, and they note that “the IPCC  calls for higher rates for the period 1993–2003: 3.1 ± 0.7.”…
Kolker and Hameed gathered long-term data regarding the Icelandic Low and the Azores High to capture variation and trend in atmospheric “Centers of Action” associated with the North Atlantic Oscillation which is regarded as “One potential driver of Atlantic Ocean sea level.” As seen in Figure 1, these large-scale features of atmospheric circulation vary considerably from year-to-year and appear to change through time in terms of latitude and longitude.
Kolker and Hameed used these relationships to statistically control for variations and trends in atmospheric circulation. They find that the “residual” sea level rise (that not explained by COA variability) in the North Atlantic lies somewhere between 0.49±0.25mm/yr and 0.93±0.39mm/yr depending on the assumptions they employ, which is substantially less than the 1.40 to 2.15 mm per year rise found in the data corrected for the glacial isostatic adjustment. This “residual” sea level rise includes both local processes such as sedimentation changes, as well as larger-scale processes such as rising global temperatures.
By the way, this forecast translates to 2-6 inches per century. This falls slightly short of the 20+ feet Al Gore promised in his movie.