A student's achievement is often the major factor in determining placement. Simply put, if a child knows "A", s/he is ready to learn "B"... when the child knows "B", s/he is ready to learn "C"... and so forth. Therefore above-level tests are useful. An above-level test would typically have a higher ceiling than a MAP test, for example. The IAS recommends an above-level test as one piece of data to consider for whole-grade acceleration.

The primary use of the PSAT which I am familiar with is for naming National Merit scholars in high school, when students are gathering credentials for college applications.

A typical response when concerned for children not having access to higher level materials is to suggest the local public library. With parental guidance, the internet can be another cost-effective educational resource for a child's particular area(s) of interest. What are your child's interests at this point in time?

What are you hoping to learn from your child taking a test?
What are you hoping your child will gain from the testing experience?