In Outlook and OWA when you are using the Multiple calendar view feature you can assign different colors to calendars within that view. (By default the calendar color is set to automatic which means a color is assigned at random) eg
When you add a Shared Calendar to your Mailbox you create a Calendar WunderBar Navigational shortcut which are documented https://msdn.microsoft.com/en-us/library/ee202589(v=exchg.80).aspx . The color that these shortcuts will be set to is set via the PidTagWlinkCalendarColor property https://msdn.microsoft.com/en-us/library/ee200641(v=exchg.80).aspx .
So if you want to set the color of one of these shortcuts with a script it does require a little bit of work. First to get the shortcut Items you need to first get the CommonViews folder and then enumerate the FAI Items collection where these shortcuts are stored. Now depending if you want to the Set the Default Folder Shortcut or a Shared Folder Shortcut (or the other calendars Shortcut for Room mailboxes and the like) you need to look at a few different properties. On Shared Calendar Shortcuts you need to look at the PidTagWlinkAddressBookEID property while on the default folder you should look at the PidTagWlinkEntryId property.
I've written a powershell module for doing this and posted it up on GitHub so with this module you can . The CalendarColor enun is mildly accurate
Set the Color of the Default Calendar Folder in a Mailbox
Set-DefaultCalendarFolderShortCut -MailboxName email@example.com -CalendarColor Yellow
(To just get the EWS Navigation Item for the default calendar folder use)
Get-DefaultCalendarFolderShortCut -MailboxName firstname.lastname@example.org
To Set the Color of a Shared Calendar folder use
Set-SharedCalendarFolderShortCut -MailboxName email@example.com -SharedCalendarMailboxName firstname.lastname@example.org -CalendarColor Yellow
You can download a copy of the module from here the code itself looks like