Testing or Quality analysis is an integral part of every production. So all applications should undergo some type of testing. It can be just developer tested, in-house tested or it can be given to a testing company. Generally, testing includes module testing, system testing, usability testing, and finally testing and certification via commonly known and industry-wide testing programs such as Symbian Signed or Java Verified for Java ME.
Nokia resources for testing: http://www.developer.nokia.com/Design/Design_process/Getting_started/Testing_usability_and_evaluation.xhtml
If you would like to test your application on various Nokia devices, visit Nokia Developer's Remote Device Access. Remote Device Access (RDA)
Java Verified: http://javaverified.com/