May 29, 2009. The UN's 2007 report tells us that before 1993 the sea level was rising 1.8mm per year (less than 1/10 inch), but from 1993 on it has been rising at 3.1mm per year. But they say they are not sure if the difference is a normal variation or part of a long-term trend. A long-term trend would likely mean humans.
The increased rate is 1.3mm per year, and it's been going for 16 years now, so that's a total of 1.3 x 16 = 20.8mm, which is a little less than 1 inch (25.4mm).
In detail, on page 30, the IPCC's Climate Change 2007 Synthesis Report says: "Increases in sea level are consistent with warming (Figure 1.1). [I.e., the measured increase does not argue against warming.] Global average sea level rose at an average rate of 1.8 [1.3 to 2.3]mm per year over 1961 to 2003 and at an average rate of about 3.1 [2.4 to 3.8]mm per year from 1993 to 2003. Whether this faster rate for 1993 to 2003 reflects [normal] decadal variation or an increase in the longerterm longerterm trend [likely due to humans] is unclear. [my comments in brackets.]
But I have measured the UN's graphs, and it looks like humans could have caused as much as 3 inches of sea level increase. The UN detects no human warming before 1950, so I drew a straight line through the sea level graph from 1870 through 1950 and found where we would have been in 2009. We are actually about 3 inches above that straight-line projection. Because the sea level graph tilts upward too suddenly in 1950, this looks to me like it's an over-estimate and the UN does not suggest such a high value. So I would say 3 inches is an upper limit, and the true answer is quite likely at least an inch less.