The solar wind interacts very strongly with the extensive cometary coma, and the various interaction processes are initiated by the ionization of cometary neutrals. The main ionization mechanism far outside the cometary bow shock is photoionization by solar extreme ultraviolet radiation. Electron distributions measured in the vicinity of comets Halley and Giacobini-Zinner by instruments on the VEGA and ICE spacecraft, respectively, are used to calculate electron impact ionization frequencies. Ionization by electrons is of comparable importance to photoionization in the magnetosheaths of Comets Halley and Giacobini-Zinner. The ionization frequency in the inner part (radial distance ≈ 10⁴ km) of the cometary plasma region of comet Halley is several times greater than the photoionization value. Tables of ionization frequencies as functions of electron temperature are presented for H₂O, CO₂, CO, O, N₂, and H.