Andrea..there is a so-called "humane" trap that lures the rodent in, closes a door, but doesn't kill it, so you can release it in a field etc...

I can get you the name.  However, I tried it for a week one time when I had a mouse in the house and the mouse never went in.  Then, reluctantly I got a "slammer" type trap that does the deathblow, but leaves the creature in a tunnel type contraption for easy disposal.  It worked first time...but I felt heartsick next morning.  The little mouse was dead allright, but had somehow struggled out of the thing and lay beside, not inside as promised.   Such a cute l'il mouse.  I buried it out back.  Why did they have to be so cute?

As for rats.  Well...I had rat "pets" for a very brief time when I lived in Calgary doing some medical training.  My roomate was a lab researcher, and he didn't have the heart to euthanize one of his subjects...a pregnant female white rat.  Sooo...he brought it home in a cage, and she promptly gave birth.  Verrrry cute little pink things they were.   I didn't realize rats could be so adorable, but...well... And, they are very intelligent as far as rodents go. 

Sooo...good luck with the rat "relocation".