I don't use the two words very much. I know "conceive" is sometimes used when a woman gives birth, but it also means to develop an idea or thought. The word "conceptualize" seems to mean the same thing. For example, "He conceived a plan to take over the world" vs. "He conceptualized a plan to take over the world". When is it appropriate to use one rather than the other?
Why waste the time and ink? I can't imagine ever using "Conceptualize" writing or speaking. Conceptualize doesn't roll of the tongue like conceive does. I can think of several nouns that have been "Converted" to useful verbs by adding ize but "Conceptualize" looks like a waste when conceive works just fine. Of course, this is just my humble opinion.
I imagine a university professor using the word "conceptualize" and his students laughing at him for his pompous vocabulary. They'd be saying "Hey! Did you envisualize how Professor Smith walkificated into the classroomular spaceularity? I can't conceptualize anything more laugh-provokingly humularious!" Try not to use "conceptualize." "Conceive" is much better, almost always.
The one instance I could imagine "conceptualize" proving useful might be with a character with the habit of speaking in sludgy verbiage -- say, a bureaucrat or a human resources executive. Aside from that sort of circumstance, conceive is far superior, as others have already noted.
i agree with the scrabble comment... using ten dollar words when dime ones work best smacks of pretentious pomposity to me, as an editor and a reader...