On a notoriously short and twisty track, the Louth racer suffered from technical problems with the Smiths Racing BMW and was unable to match the pace of the leading pack.
Hickman made it through to the second phase of qualifying, but was placed 16th and started race one from a lowly sixth-row grid position.
Digging deep, he powered his way through to complete the 30-lap affair in 10th, to pick up six championship points.
Hickman was placed on the fourth row for race two, and again had to force his way through the field, but lost a place to James Ellison on the first lap.
He circulated in 13th through to 19th lap when he benefitted from the retirement of Josh Brookes.
On lap 24 he passed Luke Mossey, and when Brad Ray retired on lap 26 he was elevated up to 10th to pick up another six points, which moved him up the rider standings to 11th on 52 points.
He said: “It’s been a really tough weekend for myself and the team so a massive thank-you to them as they have really dug deep and worked hard over the entire weekend to try and find out what we were missing.
“We never quite found it, but we did improve, and considering we were so far back in qualifying, to take two 10th places is OK as it could have been a lot worse. We will work hard again to ensure Brands Hatch is better.”
The next round is at Brands Hatch on the full circuit over the weekend of July 20 to 22.