An oscilloscope would be the best method.
Most multimeters are too slow to capture the rapidly changing voltages of an RS-232 signal. They are, however, pretty good at measuring average values. So if you send a stream of the same character you should (theoretically) be able to compute the average voltage as a function of the following voltages:
V_idle - voltage used when idle
V_space - voltage used for a space (logical 0) - between +3 and +15V
V_mark - voltage used for a mark (logical 1) - between -15 and -3V
(Usually V_idle is the same as V_mark, but, of course, you can measure V_idle on a quiet line.)
This combination will depend on the character format -- number of start bits, stop bits, data bits -- and the actual character data being sent.
See this page for how the character format is translated into voltages:
https://www.best-microcontroller-projects.com/how-rs232-works.htmlSo, pick a character to repeatedly send, determine the proportion of space bits to mark bits based on the character's binary value and the transmission format and measure the RS232 voltage.
Since there are two unknowns (V_space and V_mark) you will need to do this twice to get two equations.