The ultrafast coherent control of light localization in resonant plasmonic nanostructures is intricately related to the phase response of the involved plasmon resonances. In this work, we exploit the second harmonic signal generated by single optical nanoantennas subject to broadband phase-controlled femtosecond pulses to study and tailor the coherent resonance response. Our results reveal that both the spectral phase and the amplitude components associated with the plasmon resonance of arbitrary individual nanoantennas can be accurately determined.