We report on optical observations of the low-mass binary millisecond pulsar systems J0034-0534 and J2145-0750. A faint (I=23.5) object was found to be coincident with the timing position of PSR J2145-0750. While a galaxy or distant main-sequence star cannot be ruled out, its magnitude is consistent with an ancient white dwarf, as expected from evolutionary models. For PSR J0034-0534 no objects were detected to a limiting magnitude of R=25.0, suggesting that the white dwarf in this system is cold. Using white dwarf cooling models, the limit on the magnitude of the PSR J0034-0534 companion suggests that at birth the pulsar in this system may have rotated with a period as short as 0.6 ms. These observations provide further evidence that the magnetic fields of millisecond pulsars do not decay on time scales shorter than 1 Gyr. Comment: 6 pages, uuencoded, gz -9 compressed postscript, accepted by ApJL