Members of groups including Fossil Free Shropshire and Extinction Rebellion joined the protest outside Shirehall and HSBC on Friday, to demand a "fair" and "rapid transition" away from fossil fuels and towards renewable energy.
It comes as millions of people and organisations across the world are taking action this weekend to coincide with the UN Climate Ambition Summit taking place in New York.
Protests took place on Friday in London, Manchester, Leeds, Sheffield, Birmingham, York, Wrexham, Cardiff, Shrewsbury and Croydon.
The Shropshire County Pension Fund is relied on by thousands of county public sector pensioners with incomes coming from the fund's multimillion pound investments.
In Shrewsbury, campaigners and local people gathered outside Shirehall to call on the pensions committee to heed warnings from the UN and from scientists to stop financing fossil fuels.
An imitation blue heritage plaque was ceremonially presented to the pension fund, awarding it the title of “Leading local contributor to climate catastrophe and biodiversity loss”.
Linda Bromilow, from Shrewsbury, said: “It’s now 20 months since the pensions committee voted against divesting from fossil fuels.
"Over this time period, there have been many new alarming scientific reports including findings that the earth is dangerously close to many tipping points.
" Also over these 20 months, we have witnessed accelerating climate impacts around the world including devastating floods in Pakistan; apocalyptic wildfires in Canada, Greece and Hawaii; heatwaves reaching 40-50°C; prolonged droughts and crop failures.
"How much worse does it have to get before the committee acts responsibly in the light of this accelerating emergency?”
Later in the morning, Extinction Rebellion members gathered outside HSBC and handed in a letter to the management demanding that the bank stop funding coal, oil and gas projects and that it commits to not providing funding to the proposed West Cumbria coal mine.
Campaigner Gill Davis added: “Today we put a clear message to HSBC: 'No New Coal'.
"Banks like HSBC need to stand on the right side of history and reject any support for the West Cumbria coal mine. We can’t open any new coal mines and avoid climate breakdown.”
A spokesperson for HSBC said: “In line with our updated energy policy, HSBC will no longer provide new finance or advisory services for new oil and gas fields and our existing policies prohibit the financing by HSBC of any new coal mining activity.
"We are committed to working with clients who are playing an active role in the transition, in order to accelerate progress while maintaining energy supply and security.”
Shropshire Council, on behalf of Shropshire County Pension Fund has been contacted for comment.