I think that while APs have it good in this department, melee tanks don't. The only ones they have are 
.
Other games have utility items for non-support roles (hate to say it, but... DOTA has it) that aren't just stat-sticks.
venomous frost1 votes
BluePolarizer1 votesFist, Mallet and Heart are utility items I guess but I get them more for their raw stats. Dead Man's Plate is a purely selfish item. Supports get locket more often than tanks I think.
Drackolus2 votesTwo lockets is a good thing. You and the support won't always be in the same place, and the actives stack. Plus, you both get two aura bonuses, so that's cool.
Also, 
and even 
. I've seen it done successfully, and it's great on split-pushing tanks. Shove a lane, and when a teamfight starts drop one down and join them. They can't win that fight AND save the tower.
Come to think of it, you could totally go 
. More sightstones and sweepers help, and you would be getting that 10% quite a bit. That's also got a lot of health, armor, and magic resist, and some damage. You could swap out for if you don't want damage. All on item actives. Think outside the box.
BluePolarizer1 votesPortal is a good idea, I actually did not think about that.
Drackolus2 votesIt's one of those items that's underestimated because it's real tricky to know how to use it effectively. But if you can figure it out, it can be very strong, especially in soloQ. Think about it - it's one person doing something that the enemy team has to work together to deal with. 
works the same way, and people have been building that in soloQ since it was reworked.
BluePolarizer2 votesI actually think that portal can be a great asset on tanky tops or jungles because of the snowball effect too: once you get ahead, you can force 5v4s with the minion snowballing, but now you can also force 5v3s with a Zzrot or get a guaranteed tower with Zzrot on an already ahead lane. Since the snowball changes are here to stay, might as well abuse them for full effect.
delonix1 votesIt depends which melee tanks you're talking about, but Sion, for example, can pick up Executioner's Calling/Mortal Reminder and apply Grievous Wounds to a bunch of people in teamfights if your adc has decided they have better things to get. It's obviously not nearly as good on an AP tank like Maokai, but even then you would be applying Grievous Wounds to whoever you are sitting on every time you auto attack.