Hi Calvus,
Do you mean you prefer use a self-designed web application to send email by SMTP protocol with Office 365 mail service?
If so, you can find more resource in the following link.
msdn.microsoft.com/.../gg490662
Moreover, you can use SMTP relay to send the mails. Or you can deploy SMTP relay and then do the testing of the web application. You can refer the following link for how to set up SMTP relay.
support.microsoft.com/.../2600912
Thanks,
Ray Yang