Small solar panel + ultracapacitor + zener
You can use a precision shunt regulator to create a "zener " with a sharp voltage regulation commencement point. The TL431 (>= 2.5V ) or TLV431 (>= 1.25V) are low cost and will do what you want well.

Be aware that the voltage drop in the Schottky isolation diode D1 decreases with decreasing current and may be much less than the typically 0.3V seen at currents of 10's of mA. This can mean that a 4V PV panel voltage clamp might deliver almost 4V on the supercap. Allow enough tolerance to avoid damaging the capacitor. 

Be aware that Schottky diodes can have very greatly increased leakage currents at elevated temperatures. If the diode was adjacent to the PV panel and in full sun this may be of relevance in some cases. 

The use of diode D1 is wise in this case, but in some systems may not be strictly necessary. PV panels that are illuminated at very low light levels have low reverse currents and will not discharge a directly connected capacitor as rapidly as may be expected.