I use Comodo Internet Security Premium 4.1 and the firewall seems to block Home Sharing (to share media in your house to other computers running iTunes). When I disable CIS Firewall it works fine.
First make the home sharing executable(s) trusted program under Firewall → Advanced → Network Security Policy → Application Rules.
Then show me a screenshot of your Global Rules (Firewall → Advanced → Network Security Policy).
I have managed to fix it by doing the ‘Stealth Port Wizard’ then selecting ‘Alert me to incoming connections and make my ports stealth on a per-case basis’. Then when Comodo asked whether iTunes can connect to the internet simply allowed it.
Thanks for your help.
Congrats with solving it yourself. :-TU
I’m having the same issues how ever when I do the above the Stealth Ports Wizard does not remember my selection, it simply reverts back to ‘Define a new trusted network…’ option each time I open the window >:(
The Stealth Ports Wizard is a known source of confusion. The Wizard does not reflect the actual Global Rules. You will have to check your Global Rules to see the wizard did what it said it did.
Not sure what i’m looking for there how ever i’m not being prompted for anything when I open iTunes, but when the firewall is turned on the Home Sharing options still disappear 
Go to Firewall → Advanced → Network Security Policy → Application Rules. Do you see a rule for iTunes? If so set it to Trusted Application.
When you don’t see it add a rule. Choose Add → Select browse running processes (iTunes need to run) → select iTunes → choose “Use a Predefined Security Policy” → choose Trusted Application → Apply → Ok.
Does that work for you?
Worked like a charm - many thanks for your help!