He was 63 years old when he came to office (born on the 1st of July 1532) and had a beautiful wife, Morosina Morosini.
He was loved by the people, had a flawless cursus honorum in which he had been ambassador under five popes, and was also procuratore of San Marco de citra from the 1st of April 1588. Despite some misunderstandings with the papacy, his dogado was not marked by great events.
Good relations with the Papal States deteriorated due to the rejected request of Pope Clement VIII (1592-1605) to verify the faith of Senator Matteo Zane, appointed Patriarch of Venice. This was then aggravated by money issues and the imprisonment of two priests, tried and convicted for common crimes outside the canonical protocol.
The new pope, Paul V (1605-1621), tried to intimidate the Republic by threatening excommunication of the Senate and interdiction of the city if the Republic did not revoked the recently passed law on the purchase or acquisition of estate by the Church and if it failed to release the two mainland ecclesiastics arrested for common crimes, two despicable beings: the canon Scipione Saraceni (or Saraceno) of Vicenza and the Abbot of Nervesa, Count Brandolino (or Marcantonio) Bragadin. Saracens was accused of having harassed his niece, while the abbot was accused of all kinds of brutal killings and violence. The Pope argued that they had to be judged by an ecclesiastical court and issued two briefs: the first disputed the laws that required permission from the government both to build churches, monasteries, charities and the like, and for the passage of real estate from private to ecclesiastical bodies through donations. The other condemned the secular procedure initiated by the Republic against the two ecclesiastics. The document arrived in Venice on the 25th of December, but was not opened as the Doge was dying. The conflicts with the Holy See were later settled under the Doge Leonardo Donà (1606-1612).
Marino Grimani was buried in a mausoleum in the Church of S. Giuseppe di Castello and the Dogaressa joined him eight years later. The funeral monument is attributed to V. Scamozzi, but was perhaps the work of the Proto Francesco Bernardino Fossati, while the statues of the Doge and the Dogaressa were sculpted by G. Campagna.