Delayed edit: Yes, apparently tidally-locked planets can have a surprisingly large magnetic field. Evidently the major reason for planetary fields is convection, not rotation. ([0] cites [1]) However, I believe there are also homopolar [2] generation effects due to the star and the planet's (tidally locked) rotation. [3] looked at fields caused by convection due to tidal flexing. [4] talks about magnetic interactions between stars and close planets.

[0] https://www.quora.com/How-does-the-magnetic-field-of-a-star-....

[1] “Energy flux determines magnetic field strength of planets and stars”, U. R. Christensen et al, Nature vol 457, pages 167–169

[2] https://en.wikipedia.org/wiki/Homopolar_generator#Astrophysi....

[3] https://exoplanets.nasa.gov/news/217/earth-like-exoplanets-m....

[4] https://www.youtube.com/watch?v=HjfOdjpNZHo (Talk by Evgenya Shkolnik, part of Short Course on Magnetic Fields: A Window to a Planet's Interior and Habitability at the Keck Institute for Space Studies at Caltech on August 12, 2013)