Microarchitectural attacks exploit the abstraction gap between the Instruction Set Architecture (ISA) and how instructions are actually executed by processors to compromise the confidentiality and integrity of a system. To secure systems against microarchitectural attacks, programmers need to reason about and program against these microarchitectural side-effects. However, we cannot -- and should not -- expect programmers to manually tailor programs for specific processors and their security guarantees. Instead, we could rely on compilers (and the secure compilation community), as they can play a prominent role in bridging this gap: compilers should target specific processors microarchitectural security guarantees and they should leverage these guarantees to produce secure code. To achieve this, we outline the idea of Contract-Aware Secure COmpilation (CASCO) where compilers are parametric with respect to a hardware/software security-contract, an abstraction capturing a processor's security guarantees. That is, compilers will automatically leverage the guarantees formalized in the contract to ensure that program-level security properties are preserved at microarchitectural level.