The theory of relativity wasn't testable when it was first proposed. Part of the reason Einstein never got a nobel for it was that it wasn't until the 1970's that there was real firm experimental evidence for it.
There's a distinction between something that can never be tested and something that can't be tested now due to technological limitations.
You mean the observations Eddington took in 1919 confirming light bending in accordance with predictions by general relativity didn't take place? From the Wikipedia entry:
"Eddington's observations published the next year confirmed Einstein's theory, and were hailed at the time as a conclusive proof of general relativity over the Newtonian model."
Also, relativity made a number of testable predictions. From the wiki page on the theory of relativity:
"The predictions of special relativity have been confirmed in numerous tests since Einstein published his paper in 1905, but three experiments conducted between 1881 and 1938 were critical to its validation. These are the Michelson–Morley experiment, the Kennedy–Thorndike experiment, and the Ives–Stilwell experiment. Einstein derived the Lorentz transformations from first principles in 1905, but these three experiments allow the transformations to be induced from experimental evidence."
Obviously the testing of the theory still continues as we gather more data from around the universe, but to say there wasn't firm experimental evidence until the 1970s isn't correct.
Until string theory makes some testable predictions it's just mathematical and philosophical wanking.