It's a good thing, then, that there are satellites measuring the earth's gravity, temperature, and land/sea level on a global basis, not just at coastlines. Also, the position of ground-based sensors would be tracked by GPS, so one could tell if the land itself was rising or falling.

As a layperson I've learned that lot of effort goes into developing consistent, scientifically useful models of the earth's shape and position: https://en.wikipedia.org/wiki/Geodesy

The amount of science in "Climate change and ocean rising/falling discussions" makes me want to gouge my eyes out, usually they are about as scientific as pyramid power.

Did you read the linked article? Granted, a lot of popularized articles about climate change contain propagandizing and pounding of phrases like "settled science," and I don't know why that is, but that doesn't invalidate the science that actually exists. Reading a large number of climate change articles on e.g. Ars Technica leaves me with a pretty good impression of the state of actual climate science, certainly better than my impression of "pyramid power."

Edit: since the comment to which I replied was deleted I will not post the username of its author, but here is the original text:

  Plate tectonics cause land to rise/fall faster than the speed at which
  the ocean is rising/falling. Tides are affected by many factors like
  ocean currents, weather patterns, temperatures, changes in the very
  shape of the Earth itself.
  
  The land underneath, the hard bits underneath your chair is floating on
  molten metal. And the water in the ocean is floating on top of this hard
  substance that is floating on molten metal. The surface of the earth is
  in Constant change, half rising, half falling at varying rates.
  
  If the frothing bubbling iron soup under the land were to change at all
  due to gravimetric or other physical reasons, the changes in sea level
  would be far more dramatic than what is measured in the sea level
  change. You can't just go to your local beach and stick a measuring pole
  in the sand with a calendar and a clock. Likewise you can't just go to a
  thousand randomly selected beaches and run averages, why?  Because you
  are only testing the ocean's edges, you need to randomly test the depth
  of the ocean at every point.
  
  To do this right, you must actually calculate the volume of Ocean water,
  and this hurts people's brains because it is impossible and isn't good
  for FUD articles.
  
  It could very well be possible that the oceans would normally be
  receding on account of other factors, yet it is still rising from the
  perspective of beaches because the Earth is becoming more spherical.
  
  The amount of science in "Climate change and ocean rising/falling
  discussions" makes me want to gouge my eyes out, usually they are about
  as scientific as pyramid power.  I choose to ignore people who talk
  about these sorts of things because I like to learn things by proofs,
  not be taught to believe things because of propaganda and agenda driven
  fear uncertainty and doubt for the profit of unscrupulous manipulators.