Phil Flanagan was ordered to pay nearly £50,000 damages to Tom Elliott following comments he made in a tweet.
Mr Flanagan said he was unaware his tweet was libellous.
Lawyers for AIG argued that he is ineligible for cover because he knew the comments were defamatory.
They also contended that Mr Flanagan is excluded as the social media post had nothing to do with constituency or parliamentary business.
But the Sinn Féin representative for Fermanagh and South Tyrone said he was unaware the tweet was libellous - originally believing he was merely posing a question after listening to a "one-sided" radio discussion on Northern Ireland's troubled past.
The judge in the libel case said that Mr Flanagan's tweet was grossly defamatory.
Following the two-day insurance hearing at the High Court in Belfast, the judge said he pledged to deliver his verdict as soon as possible.
A High Court judge has put a stay on any payout until Mr Flanagan resolved his legal action with the  insurers.
Judgement has been reserved in a Sinn Féin MLA's legal battle with an insurance firm over its refusal to to provide cover for a libel award against him.