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.

PC Graham Thomas was leaving Asda in South Woodham Ferrers, Essex, last month when he saw the man run off.
He dropped his own shopping and gave chase but returned to find his food and hamster treats had been taken.
The shop refunded him but a Kent woman sent him a £45 postal order. He said he was "chuffed" but was sending it back.
PC Thomas had left his vegetables and hamster food at the customer service desk before heading off after the shoplifter.
More on this story and others from Essex
He did not catch him, but was doubly unhappy when he returned to find his food had been placed in a chiller cabinet - and had been taken, presumably by another shoplifter.
At the time he described it as "annoying" but said he recognised people might "find it amusing and ironic that this has happened to a copper".
Asda refunded the £18 he had spent, but he has now received a postal order and letter from a well-wisher in Kent.
She wrote: "I see on the Teletext that you had your shopping nicked while you were helping arrest someone."
The money was so he could "get some more, this time keep your eye on it".
PC Thomas said: "I'm writing her a nice letter.
"I just couldn't believe it. I'm well chuffed but I can't accept it, of course, so I am sending it back."
He said he had been told a woman had handed his shopping back in at the store, but the original shoplifter was still at large.
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.
[NEXT_CONCEPT]
An off-duty policeman whose shopping was stolen as he tried to catch a supermarket shoplifter has received a cash windfall from a well-wisher.