An ammeter measures the current flowing through it, so with no resistance its measurement would be most accurate. A voltmeter measures the difference in potential between two points, so with infinite resistance the measurement would be most accurate.
Work Step by Step
An ammeter is wired in series with a circuit element to measure the current that was flowing through it. An ideal, zero-resistance ammeter wouldn’t change the current that was originally flowing. A voltmeter is wired in parallel with a circuit element in order to measure the voltage difference across it. An ideal, infinite-resistance voltmeter wouldn’t shunt any current around the element, and thus, would not change the original voltage difference that was present.