Is there any way to determine or estimate where the cloud tops are? There are various ways to find out or at least estimate where cloud bases are, e.g. ATIS/AWOS/ASOS report them directly, PIREPs may mention them, and you can make a rough estimate based on the temperature/dew point spread.

Is there any way to determine (or estimate) where the tops are, assuming that no PIREPs are available?
https://www.aviationweather.gov/obs/radar/ provides cloud tops for weather with precipitation. 

Cloud tops with no precip can be discerned from data provided in the Skew-t log℗ charts that are part of this app http://www.skewtlogpro.com/about-skew-t-log-p-charts/

Where the temperature and dew point on the skew-t charts are converged you can expect clouds. If the convergence extends into the freezing level indicated on the chart you can expect icing.