It proved a difficult weekend for both.
Westmeath have been relegated from Division 1B of the National Hurling League.
They suffered a heavy defeat at the hands of Waterford yesterday.
The final score was 24 points to 7-34.
Laois could be joining them in Division 2A next year.
Tommy Fitzgerald's side were well beaten by Antrim.
Their 4-22 to 0-21 point loss in Corrigan Park means Laois need two wins from their last two games to ensure survival.
Offaly meanwhile have been promoted to Division 1A after Carlow's loss to Dublin on Saturday.
Westmeath manager Seoirse Bulfin says dropping from 1B is hard to take:
Our coverage of Westmeath against Waterford is with thanks to The O’Brien Motor Group Mullingar; home of the all-new 251 improved Renault Master and Renault Trafic, with advanced technology interior and more cargo space. P O Brien dot ie
Elsewhere Cork gained a measure of revenge for their defeat to Clare in last year's All-Ireland hurling final yesterday.
The visitors claimed a 6-20 to 23 points win over the Banner in their Division 1A clash at Cusack Park in Ennis.
At Nowlan Park, Kilkenny fell to a 2-25 to 1-19 defeat to Tipperary.
Athlone Town Travel To Turner's Cross For Cork City Test
Buccaneers Host Sligo In AIL
Offaly Hurlers Named In Fitzgibbon Cup Team Of The Year
Westmeath Claim Opening Round Win In Leinster Minor Football Championship
Penalty Shootout Heartache Breaks Irish Hearts In Prague
Kerry A Big And Strong Challenge For Laois - Enda Lyons
Ireland In Czechia For Crucial World Cup Play Off
NHL: Division Two Title The Goal For Laois This Weekend
Athlone Town On The Road In Women's Premier Division
Shane Lowry Begins Houston Open Hunt This Afternoon
Laois Begin U20 Leinster Football Championship With Defeat
Scheffler Drops Out As Lowry Searches For Form
Westmeath U20s Opener Postponed
Jack Carty Asked To Remain At Connacht Coaching
Laois And Offaly Open Minor Championship In Defeat
Offaly Managers Point To 'Unprecedented" Injuries In Seventh Straight Loss
Midlands Counties Enjoy Comfortable Minor Hurling Wins
Leinster Minor Football Championship Throws In
Comprehensive Mayo Win Not Enough For Westmeath
"The Lads Deserve Enormous Credit" - Laois Surpass Expectations Against Down