When it comes to checking the authenticity of a diamond - diamond pen tester is the most commonly used tool. However, the only way to be 100% sure in the quality of a diamond is by grading it at a well known gemological lab.
Why? Due to the applied technology.
Diamond pen-testers are made to check electro and heat- conductivity. They operate by sending heat or electrical charge and measuring how well any particular gemstone conducts them. Since diamond is an excellent electrical insulator, sending a current will do nothing to it – confirming its authenticity.
Since HPHT process requires small amounts of metal to be used as a catalyst for growth, this metal may get into the crystal structure of a finished rough diamond - resulting in a false reading as moissanite. Same thing happens to blue mined diamonds though - they conduct electricity due to their boron content and also read as moissanite.
It may also happen that checking different zones of the same stone may lead to different results. Another great reason not to use any pen tester is its inability to detect CVD coated moissanite.
Any reputable gemological laboratory would use more sophisticated equipment (Raman spectroscopy, photoluminescence, X-ray etc.) to test lab-grown diamonds and they would confirm that they are indeed real diamonds