How can I measure the mass of eclipsing binary stars?
It depends.

For many categories of stars, it is possible to determine the approximate mass of the star from its non-redshifted spectrum. Stars on the main sequence: this table of spectral classifications lists the approximate mass for the various classifications. A more precise mass estimation should be possible with a more precise classification. Sol, for example, is a G2, near the high end of G, putting it near the top end of the range (0.80 - 1.04 stellar masses).