He was Surgeon to the Goshawk before being appointed to the Amelia in 1807. 
Below is correspondence by Captain Frederick Paul Irby relating an encounter of the Amelia with two French Frigates in 1813 in which Stephen Williamson is praised for his humane and skilful attention to the wounded.......
Admiralty-Office, March 23, 1813.
Copy of a Letter from the Honourable Captain Irby, of his Majesty's ship the Amelia, to John Wilson Croker, Esq. dated at Spithead, the 23d instant
I beg leave to acquaint you, for the information of the Right Honourable the Lords Commissioners of the Admiralty, that when I was about to quit Sierra Leone River for England, in his Majesty's ship under my command on the 29th January, Lieutenant Pascoe arrived there with the chief part of the crew of his Majesty's gun-brig Daring, he having been obliged to run his vessel on shore, and blow her up at Tamara (one of the Isles de Loss), in consequence of having been chased by a French frigate, in company with two other ships, apparently frigates; he reported having left them at anchor off the islands on the 27th.
I immediately dispatched Lieutenant Pascoe in a small schooner to reconnoitre the enemy (he having volunteered his services), and on the 3d February he returned, having ascertained their force to be two frigates of the largest class (L'Arethuse and Le Rubis,), and a Portuguese ship, their prize; that they had nearly completed their water; and, after unloading the Portuguese ship, intended to give her up to the crew, and proceed themselves to sea to intercept our homewardbound trade.
Conceiving that if I cruized off the Isles de Loss (in the event of their not having left them), I might be enabled to fall in with any of his Majesty's ships that might be coming down the coast, and also protect the vessels bound to Sierra Leone, of which I had received intelligence, I prepared to weigh, when a cartel arrived from the islands with the master and boat's crew of the Daring, and the master and crew of another vessel they had taken, whose accounts coroborating Lieutenant Pascoe's report, I left Sierra Leone River, and worked up to the islands; standing in at daylight of the 6th ultimo towards the island of Tamara, we joined the Princess Charlotte Government schooner, who informed me one of the frigates was at anchor at a considerable distance to the northward from the other, and was apparently unloading the prize. I dispatched the schooner to Sierra Leone, to leave directions to any ships that might arrive to repair to me.
Having neared the island in the evening, the frigate to the nothwnrd weighed, and stood out to sea; the other frigate had signals flying and being observed at sunset with her topsail hoisted, I stood off for the night; and the next morning one of the frigates, (I believe L'Arethuse,) was just visible from the deck - it was then calm; on a breeze springing up about noon she stood towards us. As I had hopes of drawing her from her consort we continued standing out to sea till sun-set, when not perceiving the other ship from the mast-head, and the breeze failing, we shortened sail, w'ore and stood towards her. A little after seven the enemy observing us near him, tacked, and hoisted his colours.
At 45 minutes past seven, P. M being within pistol-shot of his weather-bow, both ships commenced firing nearly at the same time, which continued (remaining nearly in the same situation) until twenty one minutes past eleven, when she bore up, having the advantage of being able so to do, leaving us in an ungovernable state, with our sails, standing and running rigging cut to pieces, and masts injured.
During the action we twice fell on board the enemy, in attempting to thwart his hawse when he attempted to board, but was repulsed by the marines (which were commanded by Lieutenant Simpson,) and the boarders.
Though I most sincerely lament the numerous list of killed and wounded, which amount to one hundred and forty-one, yet it is the greatest consolation in reflecting that we were never once exposed to a raking shot, or the slightest accident occurred; all fell by fair fighting. It is with the most poignant regret I have to mention the names of Senior and Second Lieutenants, John James Bates and John Pope, and Lieutenant Grainger, of marines, among the slain; they fell early in the action; having been more than five years in the ship, I have had ample opportunities of knowing their inestimable characters, and the consequent loss the service has sustained by their falling. It is with equal concern I have to mention Lieutenant George Wills, the junior Lieutenant, who fell while carrying on the duty on the quarter deck, when I received a wound which obliged me to quit it ; and also of that good and zealous officer, Lieutenant Pascoe, late of the Daring, who commanded the midship guns, on the main deck; Mr John Bogue, late Purser of the Thais, (invalid) received a mortal wound below, after having been before wounded on the quarter-deck.
When I have the misfortune to state such a severe loss, I trust it will be clear every person must have done his duty; I feel most grateful to my gallant officers and crew, as well as the supernumeraries late belonging to the Daring, for their cool, steady, and persevering conduct, which was worthy the utmost success; but the superior force of the enemy, (she carrying on her main deck heavy French twenty-four pounders,) the considerable quantity of gold dust we have on board, as well as the certainty of the other frigate coming up, would have prevented me seeking a renewal of the action, if it had not been totally impracticable.
I should not omit to mention to their Lordships, the admirable conduct of Mr. De Mayne the Master, who placed the ship so ably at the commencement of the action, and his unremitting assiduity till the enemy kept away. My most grateful thanks are due to lieutenant Simpson, of Marines, and John Cullman the Purser, who exerted themselves to the utmost, as well as Mr. Saunders of the African corps. Having received the greatest assistance from Lieutenant Reeve, invalided from his Majesty's sloop Kangaroo, who was wounded more than once during the action, I have appointed him to act as first Lieutenant of the ship. Mr. Samuel Umfreville, Master's Mate, a deserving and valuable officer, as second, and Mr. Edward Robinson, Master's Mate, who has received a severe wound, as third.
The crippled state of the ship, and deplorable condition of the wounded, having rendered the object for which I sailed from Sierra Leone abortive, having every reason to conclude that the state of the enemy must have been sure, as to have greatly foiled him in his intended operations, being much cut up about his hull, I thought myself justified in not remaining on the coast, and therefore proceeded with the intention of touching at Madeira or the western islands, for refreshments for the sick, which the badness of the weather prevented, and arrived here this day.
I must not omit to report to their Lordships the high sense I entertain of the humane and skilful attention ofMr. Williamson, Surgeon, and Mr. Burke, Assistant, as also that of Mr. Stewart, late Assistant-Surgeon of the Daring, to the wounded, since this sanguinary conflict. I should also state, that although our numbers were apparently strong at the commencement of the action, yet from the length of time we had beeu on the coast, and much reduced by sickness, we had barely our complement fit for duty, and they much enervated. Herewith I transmit a list of the killed and wounded, and have the honour to be, etc, Frederick Paul Irby, Captain. Here follows a list of the killed and wounded, of which the totals are killed 51— wounded 95. (Signed) Frederick Paul Irby, Captain; Stephen Williamson, Surgeon. 
Stephen Williamson was employed as Surgeon Superintendent on the Caledonia from England to Van Diemen's Land via Rio de Janeiro in 1822.
He was included in the list of Surgeons unfit for sea in 1846.
Notes and Links
Death of the son of Stephen Williamson in Australia in 1873.- Williamson, On the 16 May at Sandhurst, Australia, David Williamson, Esq., manageer of the Bank of Victoria, Sandhurst, second son of the late Stephen Williamson, surgeon R.N., of Anstruther, Scotland. Aged 45. The Banker's Magazine Vol. 33..