Context :

Aims : We present methodology to derive high-precision estimates of the fundamental parameters of double-lined spectroscopic binaries .
We apply the methods to the case study of the double-lined \beta Cephei star \beta Centauri .
We also present a detailed analysis of \beta Centauri ’ s line-profile variations caused by its oscillations .

Methods : High-resolution spectral time series and visual or interferometric data with a good phase distribution along the orbital period are required .
We point out that a systematic error in the orbital amplitudes , and any quantities derived from them , occurs if the radial velocities of blended component lines are computed without spectral disentangling .
This technique is an essential ingredient in the derivation of the physical parameters if the goal is to obtain a precision of only a few percent .
We have devised iteration schemes to obtain the orbital elements for systems whose lines are blended throughout the orbital cycle .

Results : We derive the component masses and dynamical parallax of \beta Centauri with a precision of 6 % and 4 % , respectively .
Modelling allowed us to refine the mass estimates to 1 % precision resulting in M _ { 1 } = 10.7 \pm 0.1 M _ { \odot } and M _ { 2 } = 10.3 \pm 0.1 M _ { \odot } , and to derive the age of the system as being ( 14.1 \pm 0.6 ) \times 10 ^ { 6 } years .
We deduce two oscillation frequencies for the broad-lined primary of \beta Centauri : f _ { 1 } = 7.415 c d ^ { -1 } and f _ { 2 } = 4.542 c d ^ { -1 } or one of their aliases .
The degrees of these oscillation modes are higher than 2 for both frequencies , irrespective of the alias problem .
No evidence of oscillations in the narrow-lined secondary was found .

Conclusions : We propose that our iteration schemes be used in any future derivations of the spectroscopic orbital parameters of double-lined binaries with blended component lines to which disentangling can be successfully applied .
The combination of parameters resulting from the iteration schemes with high-precision estimates of the orbital inclination and the angular semi-major axis from interferometric or visual measurements allows a complete solution of the system .