We report new observations of the 1₁₀-1₁₁ (6 cm) and 2₁₁-2₁₂ (2 cm) transitions of ortho-formaldehyde (o-H₂CO) in absorption at z = 0.68466 toward the gravitational lens system B0218 + 357. Radiative transfer modeling indicates that both transitions are anti-inverted relative to the 4.6 K microwave background, regardless of the source covering factor, with excitation temperatures of ~1 K and 1.5-2 K for the 1₁₀-1₁₁ and 2₁₁-2₁₂ lines, respectively. Using these observations and a large velocity gradient radiative transfer model that assumes a gradient of 1 km s^–1 pc^–1, we obtain a molecular hydrogen number density of 2 × 10³ cm^-3 < n(H₂) < 1 × 10⁴ cm^-3 and a column density of 2.5 × 10¹³ cm^-2 < N(o-H₂CO) < 8.9 × 10¹³ cm^-2, where the allowed ranges conservatively include the range of possible source covering factors in both lines. The measurements suggest that H₂CO excitation in the absorbing clouds in the B0218 + 357 lens is analogous to that in Galactic molecular clouds: it would show H₂CO absorption against the cosmic microwave background if it were not illuminated by the background quasar or if it were viewed from another direction.