You can still call NIST (National Institute of Standards and Technology…the people who run the US atomic clocks) to get the time (I doubt you can get more accurate than this…it is an automated system):
303-499-7111 (Colorado)
They also have a radio broadcast.
NIST radio station WWV broadcasts time and frequency information 24 hours per day, 7 days per week to millions of listeners worldwide. WWV is located near Fort Collins, Colorado, about 100 kilometers north of Denver. The broadcast information includes time announcements, standard time intervals, standard frequencies, UT1 time corrections, a BCD time code, and geophysical alerts.
Broadcast Frequencies
WWV operates in the high frequency (HF) portion of the radio spectrum. The station radiates 10 000 W on 5 MHz, 10 MHz, and 15 MHz; and 2500 W on 2.5 MHz and 20 MHz. Each frequency is broadcast from a separate transmitter. Although each frequency carries the same information, multiple frequencies are used because the quality of HF reception depends on many factors such as location, time of year, time of day, the frequency being used, and atmospheric and ionospheric propagation conditions. The variety of frequencies makes it likely that at least one frequency will be usable at all times. - SOURCE
In general though, your phone will have near perfect time (to within a few seconds) since it is updated regularly by your cell carrier. I just called an saw my phone is a few seconds fast (like 2 seconds).