Generally, the present disclosure is directed to systems that may be used to facilitate the retrieval and/or replacement of production and/or processing equipment that may be used for subsea oil and gas operations. In one illustrative embodiment, a method is disclosed that includes, among other things, removing at least a portion of trapped production fluid (101a, 101b) from subsea equipment (100) while the subsea equipment (100) is connected to a subsea equipment installation (185) in a subsea environment (180), and storing at least the removed portion of the trapped production fluid (101a, 101b) in a subsea containment structure (120, 120a, 120b, 132) that is positioned in the subsea environment (180). Additionally, the disclosed method also includes disconnecting the subsea equipment (100) from the subsea equipment installation (185) and retrieving the subsea equipment (100) from the subsea environment (180).