This can be accomplished by going into Internet Options, selecting the security tab, then selecting "Local Intranet," sites (and selecting advanced), then adding the site you wish to save as a local intranet site.
Figure 1: Internet Explorer settings
Figure 2: Internet Options Security tab
Figure 3: Local intranet settings
Figure 4: Local Intranet site list
Chrome may save passwords automatically after you enter them the first time and select to "Save password" after seeing the prompt.
Figure 5: Save password pop-up message
Similar to Chrome, Firefox will ask if you want to save passwords automatically after you enter them the first time you access a password accessible intranet site and can be verified or updated by going to the Security settings.
Figure 6: Firefox internet options settings
Figure 7: Firefox Security settings for saved passwords