What is a reasonable approach to monitoring mechanical valve function if systemic anticoagulation needs to be held in the setting of an acute intracranial hemorrhage?  

Most modern mechanical aortic valves can tolerate being off anticoagulants for up to 2 weeks. The mitral valves however are more of a concern and I generally recommend an echocardiogram at 1 week and then reassess the risk of rebleed versus valve thrombosis.