Both sides suffered losses on Sunday.
Laois have topped their group in Division Three of the Lidl National League.
They face Roscommon in the semi-finals, despite a 2-9 to 1-11 loss to Wicklow on Saturday.
While Westmeath go up against Tipperary in a relegation play-off in Division One.
They were badly beaten 4-18 to six points by Mayo on Sunday.