"Kateřina was looking for you."
Translation:Hledala tě Kateřina.
tebe is acceptable when it is placed in the right position, and not acceptable otherwise. "tebe" is a tonic, stressed pronoun, and sounds foreign when placed in the position after the first unit of meaning, as in "Hledala tebe Kateřina.", unless it happens to be the only position left, the stressed end of the clause (so "Hledala tebe." would be an OK sentence).
tě, in contrast, is an unstressed, obligatory enclitic that normally must be placed in the position after the first unit of meaning. (and that's where you were attempting to stick the stressed alternative.)
if you don't want to deal with words like "enclitic", just try to keep tabs on words that like to hang out in the second slot, words that hate that slot, and words that don't care.