The influence of oscillating quadrupole fields on atomic energy levels is examined theoretically, and general expressions for the quadrupole matrix elements are given. The results are relevant to any ion-based clock in which one of the clock states supports a quadrupole moment. Clock shifts are estimated for +176Lu and indicate that coupling to the quadrupole field would not be a limitation to clock accuracy at the ≲10-19 level. Nevertheless, a method is suggested that would allow this shift to be calibrated. This method utilizes a resonant quadrupole coupling that enables the quadrupole moment of the atom to be measured. A proof-of-principle demonstration is given using +138Ba, in which the quadrupole moment of the D5 /2 state is estimated to be Θ =3.229 (89 ) e a02 .