In SZMJQ v Minister for Immigration (No.2)  FMCA 1137 Raphael FM suggested that public law proceedings might not be amenable to Calderbank offers, but did not decide the point.
In SZPAD v Minister for Immigration  FMCA 73, Smith FM did not explicitly decide the point but at - left open the possibility that indemnity costs might be awarded because of an unreasonable failure to accept an offer of compromise.
Neither SZMJQ nor SZPAD (insofar as it concerns this issue) appear to have been subsequently considered.
What is clear from SZMJQ at least is that any Calderbank offer must at least identify the ground upon which any offer to consent to remittal is to be based. Without this (for example, general reference to an application with multiple grounds), the Calderbank offer is uncertain and therefore cannot found a basis for indemnity costs.