simpsonocean, Welcome to Physics Forums!
This Wiki page gives a good introduction to the subject and useful information plus references:
http://en.wikipedia.org/wiki/Wave_height
See this from the United States Army Corps of Engineers' Coastal and Hydraulics Laboratory, the Coastal Engineering Manual (CEM) ,Part II, Chapter 1:
http://140.194.76.129/publications/eng-manuals/EM_1110-2-1100_vol/PartII/Part_II-Chap_1.pdf
Here are two paragraphs from the University of California, San Diego that describe types of sensors:
“There are two main types of sensors used to measure sea surface elevation, pressure sensors and buoys. Pressure sensors are mounted at a fixed position underwater, and they measure the height of the water column that passes above them. As wave crests pass by, the height of the water column increases; when troughs approach, the water column height falls. By deducting the depth of the sensor from the water column heights, a record of sea surface elevations can be generated.”
“Buoys ride atop the surface of the ocean. Equipped with accelerometers to record their own movements, buoys rise with the wave crests and fall with the troughs. Since buoys are always floating on the sea surface, by recording their own movements they are in fact recording the movements of the sea surface. Readings from the accelerometers inside the buoys can be used to calculate the buoys' vertical displacements; these values are also a record of sea surface elevation.”
http://cdip.ucsd.edu/?sub=index&nav=documents&xitem=waves
Wave height measurement techniques from Texas A&M University:
http://oceanworld.tamu.edu/resources/ocng_textbook/chapter16/chapter16_06.htm
Here are four manufacturers that sell wave sensors:
http://www.oconnerengineering.com/Marine/wave_height.htm
http://www.nickbelsondesign.co.uk/wave_height_sensors.HTM
http://www.oceanor.com/systems/seawatch/buoys-and-sensor/
http://www.falmouth.com/sensors/tidewavemeters.html
A do-it-yourself wave height sensor project using a tantalum wire:
http://journals.ametsoc.org/doi/pdf/10.1175/1520-0426(1995)012<0190:ANWHS>2.0.CO;2
There are also capacitive sensors. You may use Google search to find details about them.