In 1691 he was, it appears, commander of a small merchant ship, or pink, which was captured by a French privateer, and which he recaptured in the night with the aid of a boy; clapping on the hatches, it is said, and overpowering and throwing overboard the sleeping watch.
At La Hogue the Mary galley was tender to the admiral, and ‘was sent the first express to the queen with the news of beating and burning the enemy's ships, for which,’ wrote Griffith nine years afterwards, ‘her majesty ordered me a royal bounty of 300l., which as yet I have not received.’ He was then employed in convoy service to Newfoundland and to Lisbon, in cruising on the coast of France for intelligence, and at the bombardment of St. Malo with Benbow, after which he was sent into the Mediterranean, and early in 1695, being then at Cagliari, was ordered by Russell to go to Messina, to take command of the Trident, a French ship of 54 guns, which, together with the Content, had lately been captured by an English squadron.
Early in the voyage the ship lost her rudder; she was very weak-handed, many of her men sick, and thus, one dark night in November, as she made the coast of Ireland, she struck on a rock, and was for some time in imminent danger.
‘Not knowing where we were,’ wrote Griffith, ‘and having no boat or any other ways of saving a man, I thought I could not do too much to save the king's ship and all our lives; and then, with my cane in one hand, and a case knife in the other, to cut down their hammocks, did rouse up as many men as I could, and with God's assistance got her off, and next day into Baltimore, and after to Spithead.’ There a complaint was laid against him for, among other things, not ‘carrying a due discipline in his majesty's ship, for beating the officers, and for running up and down the deck with a case knife in his hand,’ and, being tried on these charges, was found guilty and suspended during the pleasure of the admiralty.
During 1705 he was employed on impress service, and in the beginning of 1706 was appointed to the Swiftsure, in which, in company with the Warspite, he sailed from Plymouth on 19 February 1706–7, in charge of a convoy of thirty-three merchant ships bound for Lisbon.
On 22 February they fell in with a squadron of seventeen French ships of war, many of them large; and Griffith, after consulting his officers, decided that it was hopeless to resist such an enormous superiority of force.
Griffith continued in the Swiftsure till July, when he was appointed to the Captain, in which, the following April, he took out a convoy to Lisbon, and went thence to the Mediterranean with Sir John Jennings.