We present an implementation of time-dependent linear-response equations for strongly orthogonal geminal wave function models: the time-dependent generalized valence bond (TD-GVB) perfect-pairing theory and the antisymmetrized product of strongly orthogonal geminals. The geminal wave functions are optimized using a restricted-step second-order algorithm suitable for handling many geminals, and the linear-response equations are solved in an efficient way using a direct iterative approach. The wave function optimization algorithm features an original scheme to create initial orbitals for the geminal functions in a black-box fashion. The implementation is employed to examine the accuracy of the geminal linear response for singlet excitation energies of small and medium-sized molecules. In systems dominated by dynamic correlation, geminal models constitute only a minor improvement with respect to time-dependent Hartree-Fock. Compared to the linear-response complete active space self-consistent field, TD-GVB either misses or gives large errors for states dominated by double excitations.