Both my company/department and an affiliated entity are in an IA proposal and want to provide IKOP. Do we both need to apply for BIC membership? Do we need two separate certificates?

Yes to both questions. 

Only contributions from BIC members contribute to IKOP. While BIC membership extends to all legal entities within a group of companies or institution, the name and PIC number of the legal entity appearing in the proposal need to match the one on the BIC membership certificate. Hence, each legal entity appearing in a proposal and wishing to contribute IKOP must possess a unique BIC membership certificate.

If one of the two entities is already a BIC member: please apply the procedure described in the answer to the question above: "My company/department is not a BIC member but is linked to a different legal entity that is a BIC Member. Do I need a separate BIC membership certificate to provide IKOP in an IA proposal?"