term for "finding correct solution by excluding wrong solutions"

The phrase Process of elimination is quite normal to native English-speakers, I think the meaning of what you want would be understood perfectly with this phrase. Was there a particular sentence you wanted to use with this word/phrase, which you found awkward?

In the field of medicine, I have heard this called ruling out (general form: to rule (something) out).

Examples:

A doctor would run through a series of tests, ruling out a number of incorrect diagnoses, and would be left with the correct diagnosis.
        —Validity of a Set of Clinical Criteria to Rule Out Injury to the Cervical Spine in Patients with Blunt Trauma

Another idiomatic English phrase which could fit is trial and error though this can imply some naivety or randomness in the selection of possible solutions

Another term used in medicine is differential diagnosis

http://en.wikipedia.org/wiki/Differential_diagnosis