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1. To cause something to become physically harder or more solid. In this usage, a noun or pronoun is used between "harden" and "up." The tub of ice cream was melting, so I stuck it in the freezer to harden it up.
2. To become physically harder or more solid. If the ice cream is melting, stick it in the freezer for a bit so it hardens up.
harden something up
to make something hard or strong. Put the meat in the freezer awhile to harden it up before you try to slice it thin. Harden up the ice cream a little in the freezer.