When using Safari Web Inspector to read the JavaScript console output, the log is reset upon navigation i.e. going from page index.html to mail.html clears the console output. In the Chrome Developer Tools, I can easily preserve the log by right clicking on the console space and selecting Preserve Log Upon Navigation. With this option, console log output remains intact until I manually clear the output simplifying the process of debugging JavaScript that refreshes or redirects to another page.
Is there a similar feature in Safari Web Inspector?
I don't know when this was added, but it is present in Safari on El Capitan (Safari 9.0). It works the same as in Chrome (right click in the console window and select "Keep Log on Navigation").
Update: As per Daniel Compton's answer, in Safari 11+ this is now under the settings icon as 'Console: Clear when page navigates'.
In Safari 11.1.2 they moved it again(!) back to the Console tab under the "Preserve log" checkbox. The Network log has similarly moved back to the Network tab.
In Safari 11 they moved it to the Settings panel under "Console: Clear when page navigates". It also has a sister setting "Network: Clear when page navigates".
No, there is no such feature (in Safari 5.0 at least). Looking at some Google results, I don't think this feature exists in any Safari version.