  Self-testing is the strongest form of quantum functionality verification
which allows a classical user to deduce the quantum state and measurements used
to produce measurement statistics. While self-testing of quantum states is
well-understood, self-testing of measurements, especially in high dimensions,
has remained more elusive. We demonstrate the first general result in this
direction by showing that every real projective measurement can be self-tested.
The standard definition of self-testing only allows for the certification of
real measurements. Therefore, our work effectively broadens the scope of
self-testable projective measurements to their full potential. To reach this
result, we employ the idea that existing self-tests can be extended to verify
additional untrusted measurements. This is known as `post-hoc self-testing'. We
formalize the method of post-hoc self-testing and establish a sufficient
condition for its application. Using this condition we construct self-tests for
all real projective measurements. Inspired by our construction, we develop a
new technique of iterative self-testing, which involves using post-hoc
self-testing in a sequential manner. Starting from any established self-test,
we fully characterize the set of measurements that can be verified via
iterative self-testing. This provides a clear methodology for constructing new
self-tests from pre-existing ones.
