The annual report of Aberdeen-based Faroe Petroleum shows Mr Stewart saw his salary increase by 6%, to £355,000 from £335,000 in 2012.
His salary has increased by 2.75% this year to £365,000.
His bonus increased by 23% annually in 2013, to £124,000 from £101,000.
But the total pay and benefits received by Mr Stewart were worth £553,000 in 2013 compared with £567,000 in the preceding year.
He had received a one-off payment of £67,000 in 2012 in compensation for the absence of any share incentive scheme awards.
In May 2012 Faroe scrapped plans for a new exceptional performance incentive plan, following the so-called shareholder spring of investor unrest about executive pay.
Some shareholders and corporate governance experts criticised the scheme proposed for its generosity, dilution of existing investors, reliance on share price returns, and for potentially paying out after a takeover.
The company introduced a replacement incentive plan under which executives can be awarded shares worth up to 250% of their salaries.
The company won backing from 68.1% of votes cast on the scheme at last year's general meeting while 31.9% were opposed.
Mr Stewart was awarded shares worth £887,500, the maximum possible, in July. The awards will paid in July 2016, subject to performance.