I was invited in to pitch story ideas to Ron Moore at ST:TNG. Before pitching, Paramount sent me a number of documents on the series, including "Star Trek: The Next Generation Writers' Technical Manual, Fourth Season Edition" by Rick Sternbach and Mike Okuda. In other words, this is what every writer for the series was expected to follow in regards to technical issues.
On page 15, under "Battle Configuration (Saucer Sep)," there is a sub-section, "Saucer section (aka primary hull)" that states:
When separated from the battle section (which contains the warp drive), the Saucer section is incapable of warp speed. The saucer section does have its own set of impulse engines for slower-than-light travel, and it has a complete set of deflector shields and phaser banks. When separation occurs at warp speed, the residual warp fields can take several minutes to fully collapse, so the primary hull can "coast" for some distance before it goes sublight. Control of the saucer section is managed from the main bridge.
So, at least according to the guys making this stuff up, it has no way to maintain a warp field, but will coast in one from separation until the field dissipates.