What about the WR Dictionary entry for correspond?
No help with prepositions there.
1. To answer to something else in respect of fitness; to agree with; to be agreeable or conformable to; to be congruous or in harmony with.
2. To answer to in character or function; to be similar or analogous to (rarely with).
So I turn to New Fowler's Modern English Usage and there I find something rather more like what I was looking for.
In the senses (a) to be analogous or similar and (b) to agree in amount, position, etc, correspond is usually followed by to.
When it means (c) to be in harmony or agreement or (d) to communicate by interchange of letters, it is usually followed by with.
Here's an example in context: "How the date of the event in the Quoxodil calendar corresponds [with/to] our Gregorian calendar is a matter of debate."
I think with is correct in this case. If the calendars are different then one does not correspond to the other. A date in one of the calendars could correspond to a date in the other calendar if they mark the same day, but where a date in one calendar would fall in the other calendar is a matter of the correspondence of the one calendar with the other. So...
"Here is how the date of the battle in the Quoxodil calendar corresponds with the Gregorian calendar: Blathmoth 8 corresponds to April 16."
Corresponds with relates to how they correspond. Corresponds to implies an identity between the two.