The sea level is actually rising. But the actual speed of the rise is essentially negligible: It is 3 mm per year, that means, 30 cm per century.
It is predicted that the speed of the rising increases. But in the next century, this will nonetheless not be very much. The predicted range is from 0.3 m to 1.2 m for 2100. Worst case scenarios give 2.4 m. So, even the worst case scenario has a magnitude which can be handled by mankind with already existing technologies and without large problems. Of course, there are a lot of things which have to be done. Accurate predictions of the sea level rise for the next hundred or better two hundred years would be necessary to see what is required. This is what scientists are doing, see, for example, Katsman et al. 2011 for the Netherlands or Brammer et al. 2013 for Bangladesh. Those scientists have to take into account also various local effects which may be sometimes much larger. So, building embankments along the rivers leads to rises of the tidal range, so, increases the tidal height (which is the thing that matters). At some point in Bangladesh, this effect gives 83% of the relevant local sea level rise, which according to Pethick & Orford 2013 can reach at that point up to 3.5 m in 2100.
In particular, let's note that wherever the land already has to be protected by dikes and dams, it is not a problem at all to increase the size of these dikes 3-4 m in the remaining century.
Another established technique to handle problems with beaches causes by erosion is beach nourishment. This is a technique which has been used even by such poor states like communist Eastern Germany to improve the beaches, thus, it is affordable even for poor states. In the Netherlands, essentially all coastal erosion is compensated by such nourishment. Even if the 3 mm per year we have now become 2.4 cm per year, the amount of what has been done additionally seems negligible.
Would it be affordable to build new dikes everywhere where it is necessary to prevent large losses of productive agrarian land, say, in countries like Bangladesh? From a technical point of view, of course. As if the Netherlands, when they build their dikes during medieval times to gain areas below sea level, had better technical capabilities than Bangladesh now.
What about the worst case scenario - which would be all glaciers, in Greenland as well as Antarctica, melting completely? The melting of sea ice does not lead to a rise of the sea level. All what matters as the large amounts of land ice in Greenland and Antarctica. If the entire ice of Greenland were to melt, global sea levels would rise 7.2 m. The Antarctic ice sheet contains an amount equivalent to about 58 m of sea-level rise. All the other glaciers give less than 1%. So, this gives at maximal sea level rise of 66 m (or 216 feet, see National Geographic). What remains would be the following:
So even this worst case does not look that horrible worldwide. There are, of course, large losses of territory. But the loss of territory in itself is quite irrelevant, and, of course, compensated by the new land in Greenland and Antarctica no longer covered by ice.
The situation looks, of course, different if one looks at the details. Say, in Europe, most of Netherlands and Denmark is covered by water and such towns as Berlin, Stockholm, Helsinki and St. Petersburg are under water too:
And this will be a quite typical situation, given that the coast is a good place for building towns. So, if the coastline seriously moves, those towns will appear under water.
But before panicking about the fate of Berlin, let's take a look at the time scale. Here is a picture (from Winkelmann et al. 2015) what we have to expect during the next millenium (1000 years) for the temp of the rise of the sea level (in meter per century) in dependence on how much CO2 we burn, with burning all known fossil fuel sources on the right:
As we see, even in the worst case scenario what is predicted is a temp of 3-4 meters per century. Thus, were would be enough time to build quite big things to protect the land. For example, one could imagine that the Europeans would simply cut the connection between the Atlantic and the Baltic Sea by a big dam, making the Baltic Sea an inland sea. This could be connected with a ship canal lift to transfer ships between the Atlantic and the Baltic Sea. Then, the whole Baltic Sea level could remain unchanged.
For the coast of the North Sea one would have to do the same, only on a larger scale, as what the Netherlands are doing today. Would a dike of 70 m height on the whole North Sea coast of the Netherlands and Denmark something these countries could not afford to build if they have 1000 (thousand) years for its completion? I see no reason for such pessimism.
But what about such poor countries like Bangladesh? They will not have enough resources to build big dikes and dams, not? I don't think so. The Dutch have build dikes during medieval time, and however poor the people of Bangladesh are in comparison with Western standards, in comparison with medieval times they are very rich. Even the poor can afford to lease machines which have not even existed then. They can use modern invention like ferro-concrete for construction, which makes it much easier to construct stable dikes and dams.
Moreover, we should not forget that what happened elsewhere will happen in Bangladesh too. Namely, urbanization. Many farmers will go bankrupt and move to towns. The remaining farmers will have larger areas as well as higher productivity, and can afford investments. Technologically, it is well-known what has to be done, the Dutch have already done this in the delta of the Rhein.
In comparison with the actual situation, there would be one additional problem with 70 m high dikes, caused by the water of the rivers flowing into the sea. Actually, one can have a dam which is open at low tide and closed at high tide. This allows the water of the river to flow into the sea. But what if the sea level is even at low tide much higher than the level which is acceptable for the river, which will happen in some time if the sea level rises on a large scale?
One can minimize this by using much of it inside the land for irrigation, but there may be nonetheless a lot of water which remains (and even more if precipitation increases). But there is obviously also the dumb solution: Let's pump the whole river into the sea. Would this be possible in principle? Affordable?
Such technical proposals made by laymen usually share the property that to realize them is impossible, for some quite simple and obvious (for specialists) reasons. The costs will be usually a central point. To obtain a rough estimate of the costs, let's consider a quite stupid (expensive and inefficient) realization: Let's simply use many pumps we can buy today for our garden. Without much search, we found a pump named "Mast T 20" for 3000 Euro, which pumps with 5 kW 1200 l/min 12 m high. We find 2,200 \(m^3/s\) of water flow through the Rhein river. So we would need 110,000 of such pumps to raise the Rhein water 12 m, which would be sufficient during the next centuries. This gives \(3,000 \times 110,000 = 330\) mio € to buy the pumps and 550 MW of electricity permanently, which is approximately what 1 mio households need. That's clearly affordable.
Of course, this problem would appear for every river, and if we cut the connection between North Sea and Baltic Sea, then it appears there too, essentially for all the water from all the rivers which flow into the Baltic Sea. I have not found numbers for the whole amount. But the Rhein is a sufficiently important river so that I think this gives at least an estimate for the order of magnitude of the problem. Once the magnitude for the Rhein is far from being critical, it seems not unreasonable to assume that the magnitude for the Baltic sea will be affordable too.
So we conclude that even the worst case of sea level rise there is globally not much lost, there are even good chances that the famous European countries and cities, which would be under water in this worst case, can be protected from sinking into the sea with known affordable technologies and costs which are not astronomic at all.
Let's consider now the less extreme scenarios. Let's start with the sufficiently serious but nonetheless scenario that only the Greenland ice melts, but Antarctica remains under ice. This is a quite plausible scenario, given that the temperatures in Antarctica are much lower than in Greenland. With an increase of precipitation, there will be even more snow and ice created there. So, the increasing temperature, even if it melts the sea ice around Antarctica, may remain unable to melt the whole Antactic ice shield.
If only the Greenland ice melts, this gives a sea level rise of only 7.2 m. For this size, it would probably not be necessary to block the rivers completely and pump the water to the higher sea level. Instead, high enough dikes along the riverbanks would be sufficient.
Note that this would not be a malinvestment if later the sea level rises even higher so that this will not be sufficient anymore. In this case, one would have to start to pump the river water into the sea. But with the quite high dikes along the river, the height which has to be overcome by pumping would be reduced. So, the question when to start pumping is a pragmatical one: One increases the dikes along the riverbanks, and builds new ones where it becomes necessary, as long as this is cheaper than to start pumping the water. Once one has started to pump the water, all what has to be increased further is the big outer wall against the sea.
But what about poor countries like Bangladesh? Given that Bangladesh plays a large role in alarmist propaganda, we will consider this case separately. The basic points are, nonetheless, simple and straightforward: