I am currently reading 'Blue and Gray Navies; The Civil War Afloat" by Spencer Tucker and have so far gotten to the latter stages of the Vicksburg campaign. It's a fairly new book and anyone interested in the period naval warfare should pick it up. Some information from him relating to this topic:
-Coastal (non river) Fortresses, of earth or masonry or both, were very susceptible to being reduced by heavy Naval artillery fire (usually in conjunction with adequate amphibious forces, unless they were very significant, which was rare.
Excerpt about the assault on Port Royal: (I'm typing from the book so forgive any typos)
"The action began at 9:26 am when a IX-inch Dahlgren at Fort Walker fired on the Wabash and a gun at Fort Beauregard immediately followed suit. The Wabash returned fire, followed by the Susquehanna, and the fighting became general. After passing through the channel, the ships turned in succession according to plan, passing eigh hundred years from Fort Walker. They then circled and turned to mid channel, again following it in while engaging borth fors at long range before turning south. The second Union pass was at only six hundred yards from Fort Walker. While the Union ships poured shells into the fort, the inexperienced Confederate gunners found it difficult to hit the moving Union ships. Fire from the fort steadily dimished in intensity, and by the time the Wabash was in position to commence fire for a third time with its starboard guns against Walker, Confederate fire had entirely ceased and the engagement was over. At 11:15 am the Ottawa signaled that the Confederates had abandoned the works....." (pg.88-89)
For reference, U.S.S Wabash was a 4800 ton Screw/Steam Frigate mounting 44 guns, two X-inch rifles, twenty-eight IX-inch rifles, and fourteen VIII-inch rifles. It was joined in the assault by one frigate, three sloops, 4 gunboats, and a sailing sloop the U.S.S Vandalia, while Fts. Beauregard and Walker were small to medium size Forts mounting a combined 43 guns (only about half facing the sea).
Smaller forts were easily handled, as in the case of Ft.Clark and Ft. Hatteras during the operations against the Hatteras Inlets. And so were 'medium' forts as in the excerpt above.
-Major Coastal Fortresses were more likely to be surrendered by being cut off from supplies and isolated/encircled by either naval, or, more often, ground elements, or by direct assault with infantry and ground based siege artillery, rather than be destroyed by naval artillery alone . An example was Fort Pulaski, a large brick fort with walls almost 8 feet thick, mounting forty-eight heavy guns, and considered by Gen. Lee to be "impervious to Union attack". The army placed heavy smoothbore Columbiads and Parrot Rifles on Tybee Island - the guns opened fire on April 10, the Fort was surrendered on April 11th.
-Major River Fortresses were rarely reduced by naval fire, from guns or howitzers. Like the Major Coastal Forts (Fisher for example) they were simply by passed and cut off from supply/besieged by land forces (Island No.10,). Foote's attacks on Donelson were in fact abortive.
http://en.wikipedia.org/wiki/Image:Fort_Donelson_river_battery.jpg
-The Mortar Boats of Porter and the rest were had mixed record due to fuzing issues, and probably did more as weapons of fear and intimidation, as they were used to continually bombard targets for days and weeks at a time.
"The mortars fired at the rate of about 1 shell every ten minutes. At night, in order to provide some rest to the crews, the fired at a rate of 1 shell every half hour. For six days and nights the mortars fired 16,800 shells, almost all of them at the fort (Ft. Jackon, LA) and without notable result. The problem seems to have been fuzing, the shells either burst in the air or buried themselves in the sorth earth before exploding" (pg.195)
"One item has dissapointed me - those great mortars are a dead failure; they did nothing at all, went wild, burst in the air, and caused no apprehension at all to the garrison. I am worried about this because this is the great dependence, those 13-inch mortars, that our friends in the Gulf are looking to, to reduce the forts in the Mississippi" - Flag Officer Samuel Du Pont, Commander of the South Atlantic Blockading Squadron, commenting on the use of mortar boats against Fort Pulaski.
One final comment - the firepower that was able to be brought to bear on soft ground units from Naval artillery was significant.
-New Orleans proper was surrendered without a fight as after Farragut's ships had run Fort Jackson and St. Phillip, they could fire shot and shell into New Orleans or any troops within it with free reign.
- When General Williams three thousand man union force in Baton Rouge, LA was surrounded and backed up against the Mississippi by Confederates under Gen. Breckenridge, and their lines broken, it was the Essex
http://en.wikipedia.org/wiki/USS_Essex_(1856)
and a division of Union gunboats that held off the Confederates from capturing the Union troops, even forcing the Confederates back. Had the C.S.S Arkansas been able to attack the Union boats, it's likely the U.S troops would have been forced to surrender.
-When McClellan lost his nerve (and mind) during the Peninsula campaign, believing he was outnumbered, he withdrew across the Chickahominy to be protected by the Union gunboat division in the area -
"I would most earnestly request that every gunboat or other armed vessel suitable for action in the James River be sent at once to this vicinity, and placed under the orders of Cdr. Rodgers, for the purpose of covering the camps and communications of this army" - G. McCellan on July 1 to Flag Officer Goldsborough.