"The children felt the box."
Translation:Børnene mærkede på kassen.
I think (please correct me if I’m wrong) that “mærke” by itself means to kind of passively feel something that is not an emotion (as that would be føle), e.g. He felt the heat from the radiator - han mærkede radiators varme. Also in the meaning of “notice something”. “Mærke på” is actively feeling something or for something with your hands. “Med fingerspidserne mærkede han på bulen i panden.“ (copied from Google and Henning Mankell)
“Børnene mærkede kassen” - “The children noticed the box”
It would be like sensing the box's presence and no touching to the box occurred. 'mærke + på' is used when someone feels someone's/something's presence by touching it.
I got the information from DDO. Look at line says "GRAMMATIC" at 4th meaning of the word here: http://ordnet.dk/ddo/ordbog?select=m%C3%A6rke,2&query=m%C3%A6rke