You can melt down, but you can't melt up. You can get fed up, but you can't get fed down. But getting shot up may lead to getting shot down.
Locking something up and locking it down mean the same thing, but knocking someone up and knocking them down are very different. Getting beat up and getting beat down are similar, but standing up and standing down are not.
You can tie something up or tie it down, and those are not opposites. Closing something up is not the opposite of closing it down. You can settle up or settle down, but they are two different things, not opposites.
But when you bring your computer system up and then bring it down, those are opposites. And if you mark something down the opposite is to mark it up.
You can let up and let down, back up and back down, but you only pack up and leave not pack down and leave, give up not give down, and you can bed down even though you can't bed up. You can only open something up and not open it down.
A quarreling couple can make up but not make down (and they can make out but not make in). You can feel mixed up but not feel mixed down. Yet being shaken down can leave you feeling shaken up!
Generally things get fired up or watered down, but not fired down or watered up. You can fill a glass up, but not fill it down. You can show up for work, but not show down for work. You can look someone up, but not look someone down* -- but you can look someone up and down.
English is officially broken -- everyone gets a full refund, plus a free replacement language.
[* One person told me that he thinks "look someone down" is acceptable. To me "she stared him down" sounds fine, but "she looked him down" sounds wrong. Native speakers often disagree about borderline cases like this.]