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For help in finding a physician making appointments and general information call Riverside Nurse. Riverside Shore Memorial Hospital Exceptional care compassionate setting. Riverside Shore Memorial Hospital Your trusted destination for comprehensive medical services on the Eastern Shore. Advanced Care at RSMH As one of Riversides multiple locations for inpatient and outpatient care diagnostics rehabilitation and wellness services Riverside Shore Memorial Hospital provides care for medical and surgical patients emergency department and critical care patients newborns and patients seeking diagnostic testing.