"It was a great experience," said Finnegan, who inked a two-year contract. "I spoke with a lot of GMs, head coaches, assistant coaches, defensive back coaches and just got their perspective on what they see as far as dynamics in their room, defenses that they run ... all the questions that agents really can't answer."
The Dolphins later Friday announced the signing of free-agent offensive lineman Shelley Smith to a multi-year contract.
Finnegan, 30, played the past two years with the St. Louis Rams, who cut him following a season in which he played just seven games. He suffered a fractured orbital bone during a Sept. 26 game against San Francisco.
"You can never know how much a guy has left in the tank if he's injured," Finnegan said during a late-afternoon conference call. "I can make no excuses for the times I played on the field. At times, I played good. At times, I didn't. I was injured most of the year, so that didn't help my cause."
Finnegan is expected to compete with 2013 draft picks Jamar Taylor and Will Davis for the corner spot opposite Pro Bowler Brent Grimes, who recently re-signed.
"Nothing ever's been given to me and I don't want it (to be)," Finnegan said. "I want to come in and compete for any job of that magnitude. I hope the younger guys are coming in to compete and take Grimes' and mine position. Or if they have a position, may the best man win."
Asked if he would be healthy for the team's organized team activities in the spring, Finnegan replied: "I should hope so, or damn near close to 110 percent."
The feisty corner was a seventh-round selection of the Titans in 2006, and played six seasons in Tennessee before joining the Rams. He reached the Pro Bowl in 2008 after intercepting five passes, returning one for a 99-yard touchdown.
In his career, Finnegan has 78 passes defensed and 18 interceptions, four for touchdowns.
"He's been a tough playmaker over his career," Dolphins general manager Dennis Hickey said.
Miami also signed free-agent safety Louis Delmas to a one-year contract earlier in the week.
As for Smith, the 6-4, 312-pounder joins Miami after spending the past two seasons with St. Louis.
"Shelley is a 26-year old ascending player who will be a good fit for our offensive line," Hickey said.
Smith last season played in 14 games for the Rams at right guard. He joins a unit that has one returning starter (center Mike Pouncey) and added free-agent left tackle Branden Albert on Tuesday.
The Dolphins said they would make Smith available early next week because he was "currently on a flight for his wedding" on Friday evening.