  We analyse 55 ks of Chandra X-ray observations of the Galactic globular
cluster M13. Using the latest radio timing positions of six known millisecond
pulsars (MSPs) in M13 from Wang et al. (2020), we detect confident X-ray
counterparts to five of the six MSPs at X-ray luminosities of $L_X$(0.3-8
keV)$\sim 3 \times 10^{30} - 10^{31}~{\rm erg~s^{-1}}$, including the newly
discovered PSR J1641+3627F. There are limited X-ray counts at the position of
PSR J1641+3627A, for which we obtain an upper limit $L_X<1.3 \times
10^{30}~{\rm erg~s^{-1}}$. We analyse X-ray spectra of all six MSPs, which are
well-described by either a single blackbody or a single power-law model. We
also incorporate optical/UV imaging observations from the Hubble Space
Telescope (HST) and find optical counterparts to PSR J1641+3627D and
J1641+3627F. Our colour-magnitude diagrams indicate the latter contains a white
dwarf, consistent with the properties suggested by radio timing observations.
The counterpart to J1641+3627D is only visible in the V band; however, we argue
that the companion to J1641+3627D is also a white dwarf, since we see a
blackbody-like X-ray spectrum, while MSPs with nondegenerate companions
generally show non-thermal X-rays from shocks between the pulsar and companion
winds. Our work increases the sample of known X-ray and optical counterparts of
MSPs in globular clusters.
