The 1993 Nobel prize in physics was given for the discovery of a binary pulsar, i.e. a rotating neutron star, whose orbiting frequency was changing exactly as predicted by the general theory of relativity which says that accelerating masses emit gravitational waves, lose energy, speed up the orbiting rate, and gradually collapse onto their companion.
Now, 20 years later, astronomers found a new strange couple called PSR J0348+0432 that allows us to run these tests more accurately than ever before:
A Massive Pulsar in a Compact Relativistic Binary (preprint)7,000 light years away from Earth, there is a pulsar with a companion, a white dwarf, that make the job.
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The pulsar has radius 6 miles, weighs as two Suns (the white dwarf has 1/6 of a solar mass), and spins 25 times a second (like some movies). The orbital period of the binary system is 2.5 hours and is getting accelerated. The acceleration reduces the orbital period just by 8 microseconds a year but it's apparently possible to measure such changes accurately using telescopes.
I would say that the agreement makes it insanely unlikely that the confirmation of gravitational waves by the 1993 binary pulsar was a coincidence. There are many indirect, theoretically loaded ways to become certain that gravitational waves have to exist. However, I would say that their existence has been demonstrated by direct experiments, too. Of course that we don't really need more of such confirmations but it's still moderate fun to see when they work.
It would be much more new to detect the gravitational waves as the actual vibrations of the LIGO device or another one of this kind. It has to happen at some point. In my opinion, the importance of that moment won't be in yet another confirmation of classical general relativity which we don't really need anymore but in acquiring a new type of eyes that allow us to look in the outer space and "see" things that are much less clear than classical general relativity.