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Radiative forcing by increased atmospheric levels of greenhouse gases (GHGs) produced by human activities could lead to strongly undesirable effects on oceans and their dependent human systems in the coming centuries. Such dangerous anthropogenic interference with the climate system is a possibility the UN Framework Convention on Climate Change (UNFCCC) calls on nations to avoid. Unacceptable consequences of such interference could include inundation of coastal areas and low-lying islands by rising sea level, the rate of which could exceed natural and human ability to adapt, and ocean acidification contributing to widespread disruption of marine and human food systems. Such consequences pose daunting socioeconomic costs, for developing nations in particular. Drawing on existing literature, we define example levels of acceptable global marine change in terms of global mean temperature rise, sea level rise and ocean acidification. A global-mean climate model (ACC2), is implemented in an optimizing environment, GAMS, and coupled to an economic model (DICE). Using cost-effectiveness analysis and the tolerable windows approach (TWA) allows for the computation of both economically optimal carbon dioxide emissions pathways as well as a range in carbon dioxide emissions (the so-called ``emissions corridor'') which respect the predetermined ceilings and take into account the socio-economically acceptable pace of emissions reductions. The German Advisory Council on Global Change (WBGU) has issued several guardrails focused on marine changes, of which we find the rate and absolute rise in global mean temperature to be the most restrictive (0.2 degrees Celsius per decade, 2 degrees Celsius total). Respecting these guardrails will require large reductions in both carbon and non-carbon GHGs over the next century, regardless of equilibrium climate sensitivity. WBGU sea level rise and rate of rise guardrails (1 meter absolute, 5 cm per decade) are substantially less restrictive, and respecting them does not require deviation from a business-as-usual path in the next couple hundred of years, provided common assumptions of Antarctic ice mass balance sensitivity are correct. The ocean acidification guardrail (0.2 unit decline relative to the pre-industrial value) is less restrictive than those for temperature, but does require emissions reductions into the coming century.