Simple one for two-digit reciprocals is the "opposite compass section" method. Think of the compass as having four sections, containing headings beginning with zero, 1, 2 and 3. Whatever your heading is, the digits in the opposite quadrant will add up to the same number. You just need to remember the two opposing pairs 0 and 2, 1 and 3 ...
Eg Heading 24, recip 06, heading 13, recip 31, and so on.
Works for all combinations apart from 01/19, 10/28 and 11/29.