The phrase "to come up with something" generally has two common meanings, the first is "to think up" or to invent. For example:
- he came up with a brilliant idea.
- they came up with a plan to save the old church.
Similar phrases might be to "to dream up", "to imagine", "to cook up", "to improvise".
The second is to "be able to find" something:
- she managed to come up with the money for building materials.
- they came up with two thousand volunteers to rebuild the church.
On the other hand, as far as I understand, "mit etw. aufwarten" means "to serve something (to someone)", "to offer up", etc. - anbieten, vorsetzen. Neither the sense of inventing nor "scraping together" seems to be present.
Although one could say "my mom came up with a great meal for Christmas dinner", one would be commenting more on the creativity and effort that she put into devising it. In contrast, one would not say that a restaurant "came up with" dinner for its guests, rather, simply that it served dinner to them, since there wouldn't normally be anything remarkable or inventive about the fact that they were able to do so.
Leo has two other translations for "come up with" into German, both of which are fine, though others that would be even better - especially "etw. erfinden" and "etw. entwerfen" - are missing. The main problem though, is that the _only_ translation in Leo of "mit etw. aufwarten" into English is "to come up with", and probably in almost all cases that's not appropriate, and is misleading, as can be seen here:related discussion: aufwarten mit
p.s., it's my first time making a "wrong entry?" post, please let me know (gently!) if I did something wrong...