One way around this limitation has been to mount sensors as high as possible on a ship, whether those sensors are lookouts in crow's nests or radar mounted at the top of a mast.
Since sensor altitude makes a difference, it is very interesting to see what DARPA is playing with in ACTUV Unmanned Vessel Helps TALONS Take Flight in Successful Joint Test:
DARPA’s Anti-Submarine Warfare (ASW) Continuous Trail Unmanned Vessel (ACTUV) program has developed and built a technology demonstration vessel that is currently undergoing open-water testing off the coast of California and recently set sail with its first payload: a prototype of a low-cost, elevated sensor mast developed through the Agency’s Towed Airborne Lift of Naval Systems (TALONS) research effort.Expanding the ranges of detection through use of unmanned vessels is vital to protecting those higher value units that do contain humans.
ACTUV seeks to lay the technical foundation for an entirely new class of ocean-going vessel—one able to traverse thousands of kilometers over the open seas for months at a time, without a single crew member aboard. Potential missions include submarine tracking and countermine activities. Towed behind boats or ships, TALONS could persistently carry intelligence, surveillance, reconnaissance (ISR), and communications payloads of up to 150 pounds between 500 and 1,500 feet in altitude—many times higher than current ships’ masts—and greatly extend the equipment’s range and effectiveness.
While aloft, TALONS demonstrated significant improvements to the range of the sensors and radios it carried compared to mounting them directly on a surface vessel. For example, TALONS’ surface-track radar extended its range by 500 percent—six times—compared to its range at sea level. Its electro-optical/infrared scanner doubled its observed discrimination range. The TALONS team plugged in a commercial handheld omnidirectional radio; that radio’s range more than tripled.
UPDATE: Yes, adding altitude to ship sensors is not a new idea - see the Coast Guard's sea based aerosat program from the 1980s:
During the 1980s as a result of the increased illegal traffic of narcotics and migrants in the Caribbean, the Coast Guard established the Mobile Aerostat Program. It consisted of two shore-based units located in Key West and Miami, Florida. The units were comprised of two teams per vessel (total of five) which alternately deployed aboard Sea Based Aerostat (SBA) Platforms. Aerostats were unmanned lighter-than-air aircraft which mounted sophisticated radar and other surveillance equipment. The MAP mission was to provide continuous air and surface surveillance for other law enforcement units working in the same geographic area of responsibility. SBAs normally worked in conjunction with high and medium endurance cutters and patrol boat class vessels. Successful operations were conducted with other U. S. and foreign naval forces. From 1984 to the program's decommissioning on 31 March 1992, the Aerostats provided target information resulting in numerous drug seizures and illegal alien interdictions.
Of course, that was before we had cool, unmanned vessels to tow sensors around.