The Fieldtest app is installed on all iPhones, but it is hidden. These instructions show you how to open the Fieldtest app, and also how to display the signal strength as decibels rather than bars. (Correct as of iPhone 6 running iOS 8.3)
Open up the Phone app and enter the following code in the phone number field, then tap the call button.
You should now be in the Fieldtest app. There are various screens within the app to help with signal diagnostics.
To exit the Fieldtest app and display the signal strength as decibels hold the power button until the shutdown slider is displayed. Release the power button. Hold down the home button until you are returned to the home screen. Release the home button.
Now tap the top-left corner of the status bar to toggle the signal strength indicator between bars and decibels. This feature is persistent until you re-enter Fieldtest app and exit the normal way - by clicking the home button.
Displaying the signal strength in decibels is more precise than bars and it may help you find a stronger signal in an area of poor coverage.