When markets trade compatible products, the overall procurement efficiency can be increased by forwarding the unused bids from one market to another by a predefined market operator. This process, known as bid forwarding, is a promising way to coordinate sequential markets, especially new local markets with the existing wholesale markets. This paper describes the concept of bid forwarding and its significance in the future European electricity markets. We examine the market design conditions that enable the bid forwarding process. Using the identified conditions, we analyze the possibility of bid forwarding in two real cases: 1) between the Spanish local DSO congestion management market from the OneNet project and Spanish intraday markets, and 2) between the Finnish local TSO-DSO congestion management market from the OneNet project and the manual frequency restoration reserve (mFRR) market. We discuss the main policy implications and good market design practices that can encourage the adoption of bid forwarding in upcoming markets.