Sometimes copies of tests or measurements can be found using the ERIC database. One caveat--many of the citations you locate will be for ERIC Documents, and many of the ERIC Documents have been temporarily taken down due to privacy concerns.
Doctoral students often create instruments for their own research. Use the Digital Dissertations database to search for tests that may be contained in the appendices of dissertations.
Check the abstracts to see if a test or measurement is mentioned. Remember that the writer of the dissertation holds copyright and will need to be contacted for permission. Also, keep in mind issues of reliability and validity.
Beginning in 1994, CINAHL began indexing research instruments as a publication type. However, other CINAHL records may also include information about research instruments.
To find a work that is a published research instrument, search for the Publication Type RESEARCH INSTRUMENT. This indicates the work indexed is actually a research instrument.
Some of the instruments are included full text, others are not. If the test is not available full text, ordering and copyright information are included.