Daphne Reid, 66, died after a fire broke out at her Silverhill Park home in Enniskillen on 27 December 2015.
Her husband Franklin, who was 70, died just over a week later from injuries sustained in the blaze.
Coroner Joe McCrisken said police officers disregarded their own safety to try to rescue the couple.
He added that they should be hailed as heroes.
The fire began when a cigarette fell on to a carpet in a bedroom where Mr Reid was sleeping.
The inquest in Enniskillen on Monday heard how police officers, who were the first of the emergency services staff to arrive at the scene, did not follow official training guidelines that say all rescue attempts should be left to the fire service.
Mr McCrisken said the Police Service of Northern Ireland should consider an official recognition for the officers who tried to save the couple.
PC Daniel Finnegan broke windows to let some smoke out before attempting to enter the burning house.
He told the coroner: "It was a personal judgment call."
PC Damien Maguire also attempted to enter the house through the burning, but was prevented from doing so by thick smoke.
The coroner also praised paramedics and firefighters, one of whom entered the property without breathing apparatus to rescue Mr Reid.
Enniskillen fire station commander Padraig McKeon arrived at the scene shortly after the failed police efforts to access the pensioners.
The inquest heard that he felt able to enter the property without breathing apparatus because much of the smoke had left the building.

The 26-year-old France forward had been heavily linked with Manchester United, and said last month there was a "6/10" chance he could move to Old Trafford this summer.
But he agreed to stay at Atletico after the club had a transfer ban upheld.
"The first thing I want to do is apologise to people who misunderstood my statements," Griezmann said.
"Since I have arrived, I have given everything for my club, my colleagues and my coaching staff."
Atletico cannot sign anyone until January after failing in an appeal against a ban imposed in July 2016 for breaching Fifa rules over the signing of youth players.
Griezmann, capped 41 times, scored 26 goals in 2016-17 as Atletico finished third in La Liga behind Real Madrid and Barcelona.
He was named the third best player in the world, behind Cristiano Ronaldo and Lionel Messi, at the Ballon d'Or ceremony in January.
Griezmann, who played in France's 2-1 defeat by Sweden in World Cup qualifying on Friday, is in the squad to face England in a friendly on Tuesday.
BBC World Service's John Bennett:
For me, the most interesting piece of information about Antoine Griezmann's new contract is the release clause. The club have confirmed that it stays the same, at 100 m euros, that's around £88m.
So despite the fact that 2022 is printed on the contract, this feels very much like the Frenchman will give Atletico Madrid one more year before making the big money move we all expected him to make this summer.
For now though the Atletico fans will be delighted by Griezmann's loyalty. He said it would be a "dirty move" to leave the club in their hour of need and he has kept his word.
A coroner has praised emergency services staff who attended a house fire in County Fermanagh that claimed the lives of two people.
[NEXT_CONCEPT]
Atletico Madrid's Antoine Griezmann has extended his contract by a year, with his new deal expiring in 2022.