The 364 nm photoelectron spectra of the linear C3Si- and C4Si2-anions are reported. Accurate adiabatic electron affinities are determined: EA((3)Sigma C3Si)=2.827 +/-0.007 eV and EA(C4Si2)=2.543 +/-0.006 eV. Several vibrational frequencies for both neutral molecules are also obtained. The term energy for the first linear excited state of C3Si (either (1)Delta or (1)Sigma) is 0.274 +/-0.015 eV. For C4Si2, the term energy is substantially lower than in C3Si and vibronic interactions between the two states become stronger. Experimental results are compared with high-level ab initio calculations for C3Si (see Rintelman and Gordon, following paper) and with our own calculations for C4Si2 and its anion.