I use Bigpond Email service in Australia.
Error message said that "operation timed out waiting for a response from the sending (SMTP) server".
With Trend turned off the sending of emails works.
I don't have any problems receiving emails.
For your issue, please try the following steps and check if the same symptom occurs:
Step 1. Adjust the server timeout in Microsoft Outlook For Outlook 2013
Open your Microsoft Outlook program.
Click Tools, then select E-mail Accounts. The Account Settings window will appear.
Double-click the account you wish to change. The Change E-Mail Account window will appear.
Click More Settings. The Internet E-Mail Settings window will appear.
Click the Advanced tab.
Move the slider to the right in the Server Timeouts section.
Click OK to save your changes.
Click Next, then click Finish in the E-mail Accounts window.
If you are using another version of Outlook, please let us know.
Step 2. Changing the Settings of your Trend Micro program
Open the main console of your Trend Micro Security
Click Settings (gear-like icon)
Click Internet & Email Controls, then select Spam & Emailed Files.
Untick Check for threats in files attached to email messages.
Click Apply, then click OK to save changes.
Check if you can now send an email.
Please let us know if the above procedures work for you.
Also, thank you for being a subscriber of our premium support service! Premium Service Plan gives you 24x7 priority access to a Trend Micro support specialist. For the issue you're having, you can optionally call the Premium Service hotline directly to speak to someone live, who is also equipped with advanced tools to quickly diagnose and resolve your issues. Please find the premium service phone number in the "Call Premium Support" section in this page.