If you want to know how much a test or procedure might cost before it happens, then the time to ask for a Good Faith Estimate is the moment your doctor brings up the topic. You could ask for one estimate that factors in your insurance coverage, and another which estimates your cost if you don't go use insurance.
PROs:
Works well for procedures, diagnostic tests, etc. which are scheduled in advance
Protects the consumer from being charged any more than $400 over the estimate
Shows medical billing codes, which one may use to price shop with competing providers
Good Faith Estimates are generally provided with very quick turnaround time
Widely available
CONs:
Not intended for emergency or urgent care services. Estimates are only available for services which get scheduled in advance.