After t.thielemans' answer, I worked that just
=VLOOKUP(A1, B:C, 2, FALSE)
works fine and does what I wanted, except that it returns #N/A
for non-matches; so it is suitable for the case where it is known that the value definitely exists in the look-up column.
Edit (based on t.thielemans' comment):
To avoid #N/A
for non-matches, do:
=IFERROR(VLOOKUP(A1, B:C, 2, FALSE), "No Match")