I know you're probably not looking for a DIY LC meter now, but in case you've hit a wall, consider the LC-meter project below (or at least the oscillator part).
I'm currently implementing the LC+LM311 oscillator [on perf-board] just to validate the approach before committing further. See attachment. I'm using a bread-boarded [reciprocal] frequency counter (which I happen to have handy) but any bench counter will do. Also, I've removed the need for relays in my version; replaced with a DPDT and BJT.
See Part 1 of the video at
10:28 for the theory of operation. (
https://youtu.be/KhJiE4gL5T4?t=628)
16:26 for the six formulas involved (just one frame at
https://youtu.be/KhJiE4gL5T4?t=986)
17:54 for the algorithm on how to determine C-DUT or L-DUT (
https://youtu.be/KhJiE4gL5T4?t=1074)
To summarize:
(a) first measure the freq. without any C-DUT attached,
(b) then turn on calibration cap BJT (still no C-DUT),
(c) then, attach a C-DUT (w/o cal cap) and measure freq.; use formula 5 to determine value.
OR attach L-DUT (w/o cal cap) and measure freq.; use formula 6 to determine value.
Calibration steps (a) and (b) only needed every once in a while.
I've successfully measured down to 16pf (all I had) just using manual recording of the frequencies with/without DUT and calibration cap into a spreadsheet. Measuring inductors yields values close to whats printed, although, in the 10s of uH to 100mH; I don't have any nH inductors. The chosen L+C values has problems with >1uF C-DUTs so I'll be exploring other combinations to determine ranges.
FYI: I'm just a hobbyist (no EE) and as such, am not (yet) knowledgeable on the intricacies of those fancy HP LCR meters on eBay. But this appears to fit my C and L measurement needs and may be worthwhile for you. Also, in case you're wondering, the reciprocal frequency counter on the b-b [74HC4020+74HC74+ATTINY84] is based on
www.instructables.com/High-Resolution-Frequency-Counter/ (good to 7 digits) but I've done a major rewrite of the software.
Original LC meter project links:
Hackaday IO:
https://hackaday.io/project/178081-build-an-lc-meterGithub:
https://github.com/coreWeaver/LC-MeterLook for parts 1 thru 5:
https://www.youtube.com/channel/UCSwxZFW1XBvgM92nI7XMwSA/videos Measuring Femto Farads: