The visitors had a goal disallowed in the first half when Stina Blackstenius' header was ruled out for offside.
Gilly Flaherty then tripped Lotta Schelin in the area but Chamberlain saved Kosovare Asllani's penalty.
England manager Mark Sampson had made 10 changes to the side that lost to Norway on Sunday.
The Lionesses looked sharp and enjoyed good passages of play but found clear-cut chances hard to come by against the Rio Olympics silver medallists.
England's best effort fell to captain on the night Jordan Nobbs, whose powerful shot from the edge of the area curled just wide of the post.
As expected with Women's Super League clubs only returning to training two weeks ago, Sampson made wholesale changes to the team, with only Chamberlain retaining her place.
The Liverpool goalkeeper once again impressed, making a string of quick reaction saves from close range as well parrying away the late penalty.
In her first England appearance in almost four years, Rachel Williams dominated the midfield, winning challenges all over the pitch.
The Notts County player, who also works as a plasterer, displayed power and strength across the 90 minutes.
With usual skipper Steph Houghton starting on the bench, Nobbs led the side and the Arsenal midfielder distributed the ball well under pressure.
And Chelsea's Millie Bright defended bravely on her first senior England start.
England now have a five-week break before they take part in the SheBelieves Cup in the United States.
They will take on the three top-ranked teams in the world; USA, Germany and France.
England face France in their opener on 1 March in Pennsylvania.
They then face the hosts in New Jersey on 4 March and European champions Germany in Washington on 7 March.
Following that, Sampson's squad are expected to play several other friendlies before their Euro 2017 campaign gets under way against Scotland on 19 July in the Netherlands.
In the meantime, the Women's Super League Spring series begins in April.
Match ends, England 0, Sweden 0.
Second Half ends, England 0, Sweden 0.
Attempt saved. Nilla Fischer (Sweden) left footed shot from the centre of the box is saved in the bottom left corner.
Lotta Schelin (Sweden) wins a free kick on the right wing.
Foul by Millie Bright (England).
Attempt missed. Gemma Davison (England) right footed shot from outside the box is high and wide to the right following a corner.
Corner,  England. Conceded by Caroline Seger.
Rachel Williams (England) wins a free kick in the attacking half.
Foul by Hanna Folkesson (Sweden).
Offside, England. Gilly Flaherty tries a through ball, but Demi Stokes is caught offside.
Foul by Demi Stokes (England).
Jessica Samuelsson (Sweden) wins a free kick in the defensive half.
Foul by Hanna Glas (Sweden).
Rachel Daly (England) wins a free kick in the defensive half.
Delay over. They are ready to continue.
Delay in match Rachel Daly (England) because of an injury.
Attempt missed. Jordan Nobbs (England) right footed shot from outside the box misses to the left. Assisted by Rachel Williams.
Foul by Hanna Folkesson (Sweden).
Isobel Christiansen (England) wins a free kick in the defensive half.
Offside, Sweden. Hanna Glas tries a through ball, but Lotta Schelin is caught offside.
Substitution, Sweden. Olivia Schough replaces Kosovare Asllani.
Substitution, Sweden. Hanna Glas replaces Jonna Andersson.
Corner,  Sweden. Conceded by Millie Bright.
Corner,  Sweden. Conceded by Siobhan Chamberlain.
Penalty saved! Kosovare Asllani (Sweden) fails to capitalise on this great opportunity,  right footed shot saved  in the bottom right corner.
Penalty Sweden. Lotta Schelin draws a foul in the penalty area.
Penalty conceded by Gilly Flaherty (England) after a foul in the penalty area.
Attempt blocked. Rachel Williams (England) right footed shot from outside the box is blocked.
Attempt missed. Isobel Christiansen (England) right footed shot from the centre of the box misses to the right. Assisted by Demi Stokes.
Substitution, England. Demi Stokes replaces Karen Carney.
Attempt missed. Pauline Hammarlund (Sweden) right footed shot from the centre of the box is close, but misses to the right. Assisted by Lotta Schelin.
Foul by Caroline Seger (Sweden).
Rachel Williams (England) wins a free kick in the defensive half.
Offside, England. Siobhan Chamberlain tries a through ball, but Rachel Williams is caught offside.
Substitution, Sweden. Magdalena Eriksson replaces Linda Sembrant.
Substitution, Sweden. Hanna Folkesson replaces Lisa Dahlkvist.
Delay over. They are ready to continue.
Delay in match Siobhan Chamberlain (England) because of an injury.
Gilly Flaherty (England) is shown the yellow card for a bad foul.
Foul by Gilly Flaherty (England).
Siobhan Chamberlain saved a penalty as England ended their pre-season training camp in Spain with a battling goalless draw against Sweden.