When a passionate playwright finds his muse in a romantic, young woman, disguised as a male actor, they engage in an affair behind the scenes of the production of Romeo and Juliet under the jealous suspicion of the annoying noble to which her aristocratic family has betrothed her.

I think the objective goal of 'Shakespeare in love' is paying off his debt.
He must write a successful play 'or else' (Goal)
but he has writer's block (Obsticle)
He discovers his muse and a forbidden love in an aristocratic lady posing as a male actor (Possible second inciting incident)
In order to succeed, her gender must be kept a secret. (Possible second obstacle)

I can see why it might be a little difficult to write a concise logline for "Shakespeare in Love"

By the 45 minute mark of the 2nd Act the affair is underway; Will has found his muse and the inspiration to write the play. ? So if finding inspiration is his objective goal, he's achieved it. ?Mission more than accomplished.

But finding inspiration is not his objective goal. ?What Will must do is write the play. ?That's his objective goal. The muse is his means to that end, to give him the inspiration to realize his objective goal.

But complications ensue such that his love life ?not only inspires but mirrors the love story -- that's the hook that sold the script. ?And it's the conceit that ?makes the film so funny and engaging to watch.

Agreed with most of what DPG and Moses99 wrote, but I think the logline can indicate more action:

After Shakespeare hits a writer's block he must find?inspiration in a passionate affair with a young royal, betrothed to another, if he is to write Romeo and Juliet.