Background
The authors write that "satellite altimetry measurements since 1993 have provided unique information about changes in global and regional mean sea levels," suggesting a mean rate of rise of 3.2 mm/yr for global sea level over the period 1993-2012 (Boening et al., 2012; Cazenave et al., 2012), which "notably exceeds the estimate of 1.8 mm/yr sea level rise for the 20th century (Bindoff et al., 2007)." So which rate is closest to the truth?

What was done
In a study designed to answer this question, Jevrejeva et al. (2014) say they "renew the global sea level [GSL] reconstruction by Jevrejeva et al. (2006), using monthly mean sea level data collected by the Permanent Service for Mean Sea Level (PSMSL) covering the observations from 1807 to 2010," thereby improving the GSL reconstruction by increasing data coverage "by using many more stations, particularly in the polar regions, and recently processed historic data series from isolated island stations," as well as by extending the end of the reconstruction from 2002 to 2009.

What was learned
Quoting the five researchers, "the new reconstruction suggests a linear trend of 1.9 ± 0.3 mm/yr during the 20th century" and "1.8 ± 0.5 mm/yr for the period 1970-2008."

What it means
Although some regions have recently experienced much greater rates of sea level rise, such as the Arctic (3.6 mm/yr) and Antarctic (4.1 mm/yr), with the mid-1980s even exhibiting a rate of 5.3 mm/yr (Holgate, 2007), this newest analysis of the most comprehensive data set available suggests that there has been no dramatic increase - or any increase, for that matter - in the mean rate of global sea level rise due to the historical increase in the atmosphere's CO2 concentration.

References
Bindoff, N.L., Willebrand, J., Artale, V., Cazenave, A., Gregory, J., Gulev, S., Hanawa, K., Le Quere, C., Levitus, S., Nojiri, Y., Shum, C.K., Talley, L.D. and Unnikrishnan, A. 2007. Observations: Oceanic climate change and sea level. In: Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K.B., Tignor, M. and Miller, H.L. (Eds.). Climate Change 2007: They Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, United Kingdom.

Boening, C., Willis, J.K., Landerer, F.W., Nerem, R.S. and Fasullo, J. 2012. The 2011 La Niņa: So strong, the oceans fell. Geophysical Research Letters 39: 10.1029/2012GL053055.

Cazenave, A. Henry, O., Munier, S., Meyssignac, B., Delcroix, T., Llovel, W., Palanisamy, H. and Becker, M. 2012. Estimating ENSO influence on the global mean sea level, 1993-2010. Marine Geodesy 35: 82-97.

Holgate, S.J. 2007. On the decadal rates of sea level change during the twentieth century. Geophysical Research Letters 34: 10.1029/2006GL028429.

Jevrejeva, S., Grinsted, A., Moore, J.C. and Holgate, S. 2006. Nonlinear trends and multi-year cycle in sea level records. Journal of Geophysical Research 111: 10.1029/2005JC003229.