Offaly suffered defeat in the Junior Championship.
Westmeath Ladies Footballers secured their opening win of the season in the All Ireland series over the weekend.
Frank Browne’s side were convincing 3-9 to 0-4 winners over Monaghan in Cusack Park on Sunday.
They return to action away to Louth for round two this Sunday.
Elsewhere, Offaly got their Junior Championship off and running with a 4-15 to 1-9 defeat away to Antrim.
The Faithful return to action this Sunday at home to Longford, while Laois will take on Clare in the Intermediate Championship.