Context :

Aims : We aim at detecting and characterizing the main-sequence companions of a sample of known and suspected Galactic binary Cepheids .
The long-term objective is to accurately and independently measure the Cepheid masses and the distances .

Methods : We used the multi-telescope interferometric combiners CHARA/MIRC and VLTI/PIONIER to detect and measure the astrometric positions of the high-contrast companions orbiting 16 bright Galactic Cepheids .
We made use of the CANDID algorithm to search for the companions and set detection limits from interferometric observations .
We also present new high-precision radial velocity measurements which were used to fit radial pulsation and orbital velocities .

Results : We report the detection of the companions orbiting the Cepheids U Aql , BP Cir , and S Mus , possible detections for FF Aql , Y Car , BG Cru , X Sgr , V350 Sgr , and V636 Sco , while no component is detected around U Car , YZ Car , T Mon , R Mus , S Nor , W Sgr and AH Vel .
For U Aql and S Mus , we performed a preliminary orbital fit combining their astrometric measurements with newly obtained high-precision single-line radial velocities , providing the full set of orbital elements and pulsation parameters .
Assuming the distance from a period-luminosity ( P-L ) relation for both Cepheids , we estimated preliminary masses of M _ { \mathrm { U Aql } } = 4.97 \pm 0.62 M _ { \odot } and M _ { \mathrm { S Mus } } = 4.63 \pm 0.99 M _ { \odot } .
For YZ Car , W Sgr , V350 Sgr , and V636 Sco , we revised the spectroscopic orbits using new high-precision radial velocities , while we updated the pulsation parameters for BP Cir , BG Cru , S Nor and AH Vel .
Our interferometric observations also provide measurements of the angular diameters , that can be used in a Baade-Wesselink type analysis .

Conclusions : We have now several astrometric detections of Cepheid companions .
When radial velocities of the companions will be available , such systems will provide accurate and independent masses and distances .
Orbital parallaxes with an accuracy better than 5 % will be particularly useful for a better calibration of the P-L relation .
The final Gaia parallaxes will be also particularly helpful for single-line spectroscopic systems , where mass and distance are degenerate .
Mass measurements are necessary for a better understanding of the age and evolution of Cepheids .