A tubular string testing system for use with a tubular string having a longitudinally extending flow passage can include a valve which selectively permits and prevents fluid communication between sections of the flow passage, a bypass passage which provides fluid communication between the sections of the flow passage when the valve is closed, and a filter which filters fluid that flows through the bypass passage. A method of testing a tubular string can include permitting fluid to flow through a bypass passage which connects sections of a flow passage extending longitudinally through the tubular string, a filter filtering the fluid which flows through the bypass passage, a valve of a tubular string testing system preventing flow of the fluid between the sections of the flow passage through the valve, and flow through the bypass passage being prevented in response to a predetermined pressure differential being created across the filter.