First of all, I highly recommend installing an Enterprise root CA, as alluded to in the comments, because it makes certificate management loads easier. You can even script or configure automatic certificate requests and issuance policies, in addition to having a central source for certificates.
Having said that, the procedure for retrieving a machine certificate is fairly straightforward.
Log onto the machine in question. Open the Microsoft Management Console (
MMC.exe). Go to
Add/Remove Snap-in.... Select
Add ->. At the pop-up dialogue, select the
Computer account radio button, hit
Next > and select the
Local Computer radio button and hit
Finish (should be selected by default).
OK, and expand
Certificates. the one you're looking for should be under a subfolder of
Certificates, and if multiple are present, should be the one with the machine name in it, of Template type
Computer, assuming a default certificate deployment configuration. See the screenshot below.