There are no special requirements for your system to send e-mails from TestComplete. Just make sure that you specify the BuiltIn.SendMail method's parameters correctly. If you still cannot send an e-mail using the BuiltIn.SendMail method, check whether TestComplete posts any error message to the test log during the test run.
Besides the SendMail method, you can also use Collaboration Data Objects (CDO) to send e-mails from your scripts. For more information on this, see Sending E-Mail From Scripts in the online documentation.
Unfortunately, TestComplete version 6 does not support the BuiltIn.SendMail() functionality. To use this method, you need to update to the latest version of TestComplete (v. 8.6).
To help us investigate your problem with the BuiltIn.SendMAPIMail() function, please send us the code you use and the text of the exception.
Your code is correct. So, the problem is not in it.
The fact is that SendMAPIMail interacts with the mail client installed on your computer. Your mail client may incorrectly implement support for the SendMAPIMail functionality. What mail client are you using?