"Oh, I'm so sorry! Some family problems have come up and I cannot go to the meeting!"
This is one way of using "come up". It means that something has happened, usually as a surprise or unexpectedly.
"I will come up to see you tomorrow"
This is another way of saying "I will come", but with the impression that you are located either under someone (in a building with multiple levels) or south of them.
To "come up" usually refers to an action that will happen.
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"How did this problem come about?" or "The problem came about much sooner than I expected"
This usually expresses the origins of the subject. It refers to how the "problem" in the sentence began. In the second sentence, it means the problem and began sooner than what had been expected.