Offaly are in need of a win when they travel to Limerick in a fortnight.
All-Ireland Senior Camogie champions Galway endured a battling display from Offaly on Saturday.
Coming from a heavy defeat to Antrim the previous weekend, Offaly put it up to Galway but were eventually beaten 2-12 to 1-6 in Birr.
Next up for Offaly is a crucial game away to Limerick in a fortnight.
Westmeath's Intermediate Camogie team got their All-Ireland campaign off to a good start in Mullingar on Saturday.
They beat Dublin 4-13 to 1-9, and will host Galway next weekend.
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